Cohomologies of coherent sheaves and massless spectra in F-theory Outline In chapter 2 we start our journey with a revision of foundational material. As we aim at building F-theory GUT-models, it seems appropriate to start with a revision of the standard model of particle physics and grand unified theories in section 2.1. Subsequently, we turn to string theory in section 2.2 and finally F-theory in section 2.3. In particular, we will explain how Deligne cohomology can be used to model the gauge backgrounds in F-theory compactifications. We complete this chapter by reviewing zero mode counting in type IIB orientifold compactifications. As we explain in section 2.4, these zero modes are counted by sheaf cohomologies of line bundles located at D-brane intersections. Therefore, this section contains a revision of basic material on sheaves and their sheaf cohomologies. To illustrate these formal terms, we exemplify these notions for line bundles on compact, connected Riemann surfaces. We pointed out in [73] that Chow groups can describe a subset of Deligne cohomology and that they lend themselves nicely to explicit computations. The Chow group is formed from equivalence classes of algebraic cycles – two algebraic cycles are equivalent if their difference can be understood as the divisor of a rational function. In this sense Chow groups classify algebraic cycles up to rational equivalence. This definition manifestly involves rational functions, which are defined on varieties only. So in order to apply Chow groups as parametrisation of a subset of Deligne cohomology, we have to break with analytic geometry. Therefore, we explain varieties and their Chow group in detail in section 3.1. Subsequently, we argue in section 3.4 that the zero modes in F-theory vacua are counted by sheaf cohomologies of line bundles LR on the so-called matter curves CR. In phenomenological applications one wishes to compute these quantities for large numbers of explicit examples. Consequently, we set out to design computer algorithms which compute the required sheaf cohomologies. To this end, we can only allow for special geometries and will, in this thesis, focus on toric varieties. The required tools are introduced in section 3.5. Subsequently, we study a class of toric F-theory compactifications, in section 3.6. These geometries are derived from a so-called SU(5) × U(1)X-top, which was originally introduced in [74] and has been analysed with more refined techniques in appendix A.1. 2 In section 3.6 we derive the line bundles LR for this entire class of F-theory compactifications. To actually compute the sheaf cohomologies of these line bundles, we need more refined techniques. These we introduce in chapter 4. As we explain in section 3.5.1, on affine varieties coherent sheaves can be modelled by modules over the coordinate ring of the variety.3 For toric varieties there exists a similar construction – here finitely presented (f.p.) and graded modules over the coordinate ring give rise to coherent sheaves. We detail these modules in section 4.1 and section 4.2. Subsequently, we explain in section 4.3 how they encode a coherent sheaf. Finally, we apply this knowledge in section 4.4 to study an F-theory toy model. The technical steps which allow us to relate the defining data of an f.p. graded module to the sheaf cohomologies of the associated sheaf are based on theorem B.3.1, which is derived in appendix B. The subsequent chapter 5 studies far more realistic F-theory GUT models than the toy model discussed in section 4.4. While putting the finishing touches to [75], we realised that Chow groups can also help to deepen our understanding of local anomalies in F-theory. We complete this thesis by explaining this interplay in chapter 6.

Higher T-duality of super M-branes We establish a higher generalization of super L∞-algebraic T-duality of super WZW-terms for super pbranes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional geometric 11d super spacetime. "It is noteworthy that this is a derivation of M-theoretic structure from first principles, not involving any extrapolation from perturbative string theory nor any conjectures or informal analogies from other sources."

Fluxes and Warping for Gauge Couplings in F-theory We compute flux-dependent corrections in the four-dimensional F-theory effective action using the M-theory dual description. In M-theory the 7-brane fluxes are encoded by four-form flux and modify the background geometry and Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor which also depends on the torus directions of the compactification fourfold. This dependence is crucial in the derivation of the four-dimensional action, although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are described by an infinite array of Taub-NUT spaces. We use the explicit metric on this geometry to derive the locally corrected warp factor and M-theory three-from as closed expressions. We focus on contributions to the 7-brane gauge coupling function from this M-theory back-reaction and show that terms quadratic in the internal seven-brane flux are induced. The real part of the gauge coupling function is modified by the M-theory warp factor while the imaginary part is corrected due to a modified M-theory three-form potential. The obtained contributions match the known weak string coupling result, but also yield additional terms suppressed at weak coupling. This shows that the completion of the M-theory reduction opens the way to compute various corrections in a genuine F-theory setting away from the weak string coupling limit.

Structure in 6D and 4D N = 1 supergravity theories from F-theory Abstract: We explore some aspects of 4D supergravity theories and F-theory vacua that are parallel to structures in the space of 6D theories. The spectrum and topological terms in 4D supergravity theories correspond to topological data of F-theory geometry, just as in six dimensions. In particular, topological axion-curvature squared couplings appear in 4D theories; these couplings are characterized by vectors in the dual to the lattice of axion shift symmetries associated with string charges. These terms are analogous to the GreenSchwarz terms of 6D supergravity theories, though in 4D the terms are not generally linked with anomalies. We outline the correspondence between F-theory topology and data of the corresponding 4D supergravity theories. The correspondence of geometry with structure in the low-energy action illuminates topological aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of an F-theory realization also places geometrical constraints on the 4D supergravity theory in the large-volume limit.

Wavefunctions and the Point of E8 in F-theory In F-theory GUTs interactions between fields are typically localised at points of enhanced symmetry in the internal dimensions implying that the coefficient of the associated operator can be studied using a local wavefunctions overlap calculation. Some F-theory SU(5) GUT theories may exhibit a maximum symmetry enhancement at a point to E8, and in this case all the operators of the theory can be associated to the same point. We take initial steps towards the study of operators in such theories. We calculate wavefunctions and their overlaps around a general point of enhancement and establish constraints on the local form of the fluxes. We then apply the general results to a simple model at a point of E8 enhancement and calculate some example operators such as Yukawa couplings and dimension-five couplings that can lead to proton decay.

Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs We study the coupling of MSSM fields to heavy modes through cubic superpotential interactions in F-theory SU(5) GUTs. The couplings are calculated by integrating the overlap of two massless and one massive wavefunctions. The overlap integral receives contributions from only a small patch around a point of symmetry enhancement thereby allowing the wavefunctions to be determined locally on flat space, drastically simplifying the calculation. The cubic coupling between two MSSM fields and one of the massive coloured Higgs triplets present in SU(5) GUTs is calculated using a local eight-dimensional SO(12) gauge theory. We find that for the most natural regions of local parameter space the coupling to the triplet is comparable to or stronger than in minimal four-dimensional GUTs thereby, for those regions, reaffirming or strengthening constraints from dimension-five proton decay. We also identify possible regions in local parameter space where the couplings to the lightest generations are substantially suppressed compared to minimal four-dimensional GUTs. We further apply our results and techniques to study other phenomenologically important operators arising from coupling to heavy modes. In particular we calculate within a toy model flavour non-universal soft masses induced by integrating out heavy modes which lead to FCNCs.

F-theory fluxes, Chirality and Chern-Simons theories Abstract: We study the charged chiral matter spectrum of four-dimensional F-theory compactifications on elliptically fibered Calabi-Yau fourfolds by using the dual M-theory description. A chiral spectrum can be induced by M-theory four-form flux on the fully resolved Calabi-Yau fourfold. In M-theory this flux yields three-dimensional Chern-Simons couplings in the Coulomb branch of the gauge theory. In the F-theory compactification on an additional circle these couplings are only generated by one-loop corrections with charged fermions running in the loop. This identification allows us to infer the net number of chiral matter fields of the four-dimensional effective theory. The chirality formulas can be evaluated by using the intersection numbers and the cones of effective curves of the resolved fourfolds. We argue that a study of the effective curves also allows to follow the resolution process at each co-dimension. To write simple chirality formulas we suggest to use the effective curves involved in the resolution process to determine the matter surfaces and to connect with the group theory at co-dimension two in the base. We exemplify our methods on examples with SU(5) and SU(5) × U(1) gauge group.

F-Theory and the Landscape of Intersecting D7-Branes In this work, the moduli of D7-branes in type IIB orientifold compactifi- cations and their stabilization by fluxes is studied from the perspective of F-theory. In F-theory, the moduli of the D7-branes and the moduli of the orientifold are unified in the moduli space of an elliptic Calabi-Yau manifold. This makes it possible to study the flux stabilization of D7-branes in an elegant manner. To answer phenomenological questions, one has to translate the deformations of the elliptic Calabi-Yau manifold of F-theory back to the positions and the shape of the D7-branes. We address this problem by constructing the homology cycles that are relevant for the deformations of the elliptic Calabi-Yau manifold. We show the viability of our approach for the case of elliptic two- and three-folds. Furthermore, we discuss consistency conditions related to the intersections between D7-branes and orientifold planes which are automatically fulfilled in F-theory. Finally, we use our results to study the flux stabilization of D7-branes on the orientifold K3×T2/Z2 using F-theory on K3 × K3. In this context, we derive conditions on the fluxes to stabilize a given configuration of D7-branes. This thesis furthermore contains an introduction to F-theory and a brief review of some mathematical background.

F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P2, P1 × P1 and the recently studied P2 (1, 1, 2), yield F-theory realizations of SUGRA theories with discrete gauge groups Z3, Z2 and Z4. This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I2-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. We also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP1 has a U(1)- gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.

Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for four-dimensional F-theory compactifications on elliptic Calabi-Yau fourfolds with rank two Mordell-Weil group. The general elliptic fiber is the Calabi-Yau onefold in dP2. We classify its resolved elliptic fibrations over a general base B. The study of singularities of these fibrations leads to explicit matter representations, that we determine both for U(1)×U(1) and SU(5)×U(1) × U(1) constructions. We determine for the first time certain matter curves and surfaces using techniques involving prime ideals. The vertical cohomology ring of these fourfolds is calculated for both cases and general formulas for the Euler numbers are derived. Explicit calculations are presented for a specific base B = P3. We determine the general G4-flux that belongs to H (2,2)/V of the resolved Calabi-Yau fourfolds. As a by-product, we derive for the first time all conditions on G4-flux in general F-theory compactifications with a non-holomorphic zero section. These conditions have to be formulated after a circle reduction in terms of Chern-Simons terms on the 3D Coulomb branch and invoke M-theory/F-theory duality. New ChernSimons terms are generated by Kaluza-Klein states of the circle compactification. We explicitly perform the relevant field theory computations, that yield non-vanishing results precisely for fourfolds with a non-holomorphic zero section. Taking into account the new Chern-Simons terms, all 4D matter chiralities are determined via 3D M-theory/F-theory duality. We independently check these chiralities using the subset of matter surfaces we determined. The presented techniques are general and do not rely on toric data.

Higgs Bundles and UV Completion in F-Theory F-theory admits 7-branes with exceptional gauge symmetries, which can be compactified to give phenomenological four-dimensional GUT models. Here we study general supersymmetric compactifications of eight-dimensional Yang-Mills theory. They are mathematically described by meromorphic Higgs bundles, and therefore admit a spectral cover description. This allows us to give a rigorous and intrinsic construction of local models in F-theory. We use our results to prove a no-go theorem showing that local SU(5) models with three generations do not exist for generic moduli. However we show that three-generation models do exist on the Noether-Lefschetz locus. We explain how F-theory models can be mapped to non-perturbative orientifold models using a scaling limit proposed by Sen. Further we address the construction of global models that do not have heterotic duals. We show how one may obtain a contractible worldvolume with a two-cycle not inherited from the bulk, a necessary condition for implementing GUT breaking using fluxes. We also show that the complex structure moduli in global models can be arranged so that no dimension four or five proton decay can be generated.

The N = 1 effective action of F-theory compactifications The four-dimensional N = 1 effective action of F-theory compactified on a CalabiYau fourfold is studied by lifting a three-dimensional M-theory compactification. The lift is performed by using T-duality realized via a Legendre transform on the level of the effective action, and the application of vector-scalar duality in three dimensions. The leading order K¨ahler potential and gauge-kinetic coupling functions are determined. In these compactifications two sources of gauge theories are present. Space-time filling nonAbelian seven-branes arise at the singularities of the elliptic fibration of the fourfold. Their couplings are included by resolving the singular fourfold. Generically a U(1)r gauge theory arises from the R-R bulk sector if the base of the elliptically fibered CalabiYau fourfold supports 2r harmonic three-forms. The gauge coupling functions depend holomorphically on the complex structure moduli of the fourfold, comprising closed and open string degrees of freedom. The four-dimensional electro-magnetic duality is studied in the three-dimensional effective theory obtained after M-theory compactification. A discussion of matter couplings transforming in the adjoint of the seven-brane gauge group is included.  

Exciting Implications for String/M-Theory from LHC Higgs Boson Data Abstract: naively, the LHC Higgs boson looks like a Standard Model Higgs boson, with no guidance to physics beyond the Standard Model, as has often been remarked. The data show that what was discovered is the true Higgs boson. If one includes the full information available, experimental and theoretical, there are actually four significant clues implied by data. They point toward a supersymmetric two-doublet decoupling theory, and a hierarchy problem solution via TeV scale supersymmetry. That in turn suggests an underlying compactified string/M theory with a de Sitter vacuum, so we can be confident that the low scale model has an ultraviolet completion.

De Sitter Space in Supergravity and M Theory Two ways in which de Sitter space can arise in supergravity theories are discussed. In the first, it arises as a solution of a conventional supergravity, in which case it necessarily has no Killing spinors. For example, de Sitter space can arise as a solution of N = 8 gauged supergravities in four or five dimensions. These lift to solutions of 11-dimensional supergravity or D = 10 IIB supergravity which are warped products of de Sitter space and non-compact spaces of negative curvature. In the second way, de Sitter space can arise as a supersymmetric solution of an unconventional supergravity theory, which typically has some kinetic terms with the ‘wrong’ sign; such solutions are invariant under a de Sitter supergroup. Such solutions lift to supersymmetric solutions of unconventional supergravities in D = 10 or D = 11, which nonetheless arise as field theory limits of theories that can be obtained from M-theory by timelike T-dualities and related dualities. Brane solutions interpolate between these solutions and flat space and lead to a holographic duality between theories in de Sitter vacua and Euclidean conformal field theories. Previous results are reviewed and generalised, and discussion is included of KaluzaKlein theory with non-compact internal spaces, brane and cosmological solutions, and holography on de Sitter spaces and product spaces.

Flux Compactifications of M-Theory on Twisted Tori We find the bosonic sector of the gauged supergravities that are obtained from 11- dimensional supergravity by Scherk-Schwarz dimensional reduction with flux to any dimension D. We show that, if certain obstructions are absent, the Scherk-Schwarz ansatz for a finite set of D-dimensional fields can be extended to a full compactification of M-theory, including an infinite tower of Kaluza-Klein fields. The internal space is obtained from a group manifold (which may be non-compact) by a discrete identification. We discuss the symmetry algebra and the symmetry breaking patterns and illustrate these with particular examples. We discuss the action of U-duality on these theories in terms of symmetries of the D-dimensional supergravity, and argue that in general it will take geometric flux compactifications to M-theory on non-geometric backgrounds, such as U-folds with U-duality transition functions.

M theory and Singularities of Exceptional Holonomy Manifolds M theory compactifications on G2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory.

Effective action from M-theory on twisted connected sum G2-manifolds We study the four-dimensional low-energy effective N = 1 supergravity theory of the dimensional reduction of M-theory on G2-manifolds, which are constructed by Kovalev’s twisted connected sum gluing suitable pairs of asymptotically cylindrical Calabi–Yau threefolds XL/R augmented with a circle S1. In the Kovalev limit the Ricci-flat G2-metrics are approximated by the Ricci-flat metrics on XL/R and we identify the universal modulus — the Kovalevton — that parametrizes this limit. We observe that the low-energy effective theory exhibits in this limit gauge theory sectors with extended supersymmetry. We determine the universal (semi-classical) K¨ahler potential of the effective N = 1 supergravity action as a function of the Kovalevton and the volume modulus of the G2-manifold. This K¨ahler potential fulfills the noscale inequality such that no anti-de-Sitter vacua are admitted. We describe geometric degenerations in XL/R, which lead to non-Abelian gauge symmetries enhancements with various matter content. Studying the resulting gauge theory branches, we argue that they lead to transitions compatible with the gluing construction and provide many new explicit examples of G2-manifolds.

M-Theory from the Superpoint The “brane scan” classifies consistent Green–Schwarz strings and membranes in terms of the invariant cocycles on super-Minkowski spacetimes. The “brane bouquet” generalizes this by consecutively forming the invariant higher central extensions induced by these cocycles, which yields the complete brane content of string/M-theory, including the D-branes and the M5- brane, as well as the various duality relations between these. This raises the question whether the super-Minkowski spacetimes themselves arise as maximal invariant central extensions. Here we prove that they do. Starting from the simplest possible super-Minkowski spacetime, the superpoint, which has no Lorentz structure and no spinorial structure, we give a systematic process of consecutive maximal invariant central extensions, and show that it discovers the superMinkowski spacetimes that contain superstrings, culminating in the 10- and 11-dimensional super-Minkowski spacetimes of string/M-theory and leading directly to the brane bouquet.

Exceptional M-brane sigma models and η-symbols We develop the M-brane actions proposed in arXiv:1607.04265 by using η-symbols determined in arXiv:1708.06342. Introducing η-forms that is defined with the η-symbols, we present U-duality covariant M-brane actions which describe the known brane worldvolume theories for Mp-branes with p = 0, 2, 5. We show that the self-duality relation known in the double sigma model is naturally generalized to M-branes. In particular, for an M5-brane, the self-duality relation is nontrivially realized, where the Hodge star operator is defined with the familiar M5-brane metric while the η-form contains the self-dual 3-form field strength. The action for a Kaluza-Klein monopole is also partially reproduced. Moreover, we explain how to treat type IIB branes in our general formalism. As a demonstration, we reproduce the known action for a (p, q)-string.

M-theory Beyond The Supergravity Approximation We analyze the four-point function of stress-tensor multiplets for the 6d quantum field theory with OSp(8∗|4) symmetry which is conjectured to be dual to M-theory on AdS7 × S4, and deduce the leading correction to the tree-level supergravity prediction by obtaining a solution of the crossing equations in the large-N limit with the superconformal partial wave expansion truncated to operators with zero spin. This correction corresponds to the M-theoretic analogue of α^03 corrections in string theory. We also find solutions corresponding to higher-spin truncations, but they are subleading compared to the 1-loop supergravity prediction, which has yet to be calculated.

A Fundamental Advance in Understanding M-Theory: an M5-Brane Model We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang–Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the ABJM model.

Evidence for M-theory based on fractal nearly tri-bimaximal neutrino mixing Developing a theory that can describe everything in the universe is of great interest, and is closely relevant to M-theory, neutrino oscillation and charge-parity (CP) violation. Although M-theory is claimed as a grand unified theory, it has not been tested by any direct experiment. Here we show that existing neutrino oscillation experimental data supports one kind of high dimensional unified theory, such as M-theory. We propose a generalization of the tri-bimaximal neutrino mixing ansatz, and we find that the latest neutrino oscillation experimental data constraints dimension in a range between 10.46 and 12.93 containing 11, which is an important prediction of M-theory. This ansatz naturally incorporates the fractal feature of the universe and leptonic CP violation into the resultant scenario of fractal nearly tri-bimaximal flavor mixing. We also analyze the consequences of this new ansatze on the latest experimental data of neutrino oscillations, and this theory matches the experimental data. Furthermore, an approach to construct lepton mass matrices in fractal universe under permutation symmetry is discussed. The proposed theory opens an unexpected window on the physics beyond the Standard Model.

GUT Precursors and Entwined SUSY: The Phenomenology of Stable Non-Supersymmetric Strings Recent work has established a method of constructing non-supersymmetric string models that are stable, with near-vanishing one-loop dilaton tadpoles and cosmological constants. This opens up the tantalizing possibility of realizing stable string models whose low-energy limits directly resemble the Standard Model rather than one of its supersymmetric extensions. In this paper we consider the general structure of such strings and find that they share two important phenomenological properties. The first is a so-called “GUT-precursor” structure in which new GUT-like states appear with masses that can be many orders of magnitude lighter than the scale of gauge coupling unification. These states allow a parametrically large compactification volume, even in weakly coupled heterotic strings, and in certain regions of parameter space can give rise to dramatic collider signatures which serve as “smoking guns” for this overall string framework. The second is a residual “entwined-SUSY” (or e-SUSY) structure for the matter multiplets in which different multiplet components carry different horizontal U(1) charges. As a concrete example and existence proof of these features, we present a heterotic string model that contains the fundamental building blocks of the Standard Model such as the Standard-Model gauge group, complete chiral generations, and Higgs fields — all without supersymmetry. Even though massless gravitinos and gauginos are absent from the spectrum, we confirm that this model has an exponentially suppressed one-loop dilaton tadpole and displays both the GUT-precursor and e-SUSY structures. We also discuss some general phenomenological properties of e-SUSY, such as cancellations in radiative corrections to scalar masses, the possible existence of a corresponding approximate moduli space, and the prevention of rapid proton decay.

Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra We analyze the structure of the family of quadratic superalgebras, introduced in J Phys A 44(23):235205 (2011), for the quadratic deformations of N = 1 space-time conformal supersymmetry. We characterize in particular the ‘zero-step’ modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of N = 1 space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate all physical states (including the vacuum state), while at the same time, superpartners do not exist.  

QUANTUM BACKGROUND INDEPENDENCE IN STRING THEORY Not only in physical string theories, but also in some highly simplified situations, background independence has been difficult to understand. It is argued that the “holomorphic anomaly” of Bershadsky, Cecotti, Ooguri, and Vafa gives a fundamental explanation of some of the problems. Moreover, their anomaly equation can be interpreted in terms of a rather peculiar quantum version of background independence: in systems afflicted by the anomaly, background independence does not hold order by order in perturbation theory, but the exact partition function as a function of the coupling constants has a background independent interpretation as a state in an auxiliary quantum Hilbert space. The significance of this auxiliary space is otherwise unknown.

No, string theory does not need SUSY: Calabi-Yau compactifications of non-supersymmetric heterotic string theory Phenomenological explorations of heterotic strings have conventionally focused primarily on the E8×E8 theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16)×SO(16) theory and the related supersymmetric E8×E8 and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the nonsupersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion-couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five branes in the SO(16)×SO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.

Solving M-theory with the Conformal Bootstrap We use the conformal bootstrap to perform a precision study of 3d maximally supersymmetric (N = 8) SCFTs that describe the IR physics on N coincident M2-branes placed either in flat space or at a C 4/Z2 singularity. First, using the explicit Lagrangians of ABJ(M) [1,2] and recent supersymmetric localization results, we calculate certain half and quarter-BPS OPE coefficients, both exactly at small N, and approximately in a large N expansion that we perform to all orders in 1/N. Comparing these values with the numerical bootstrap bounds leads us to conjecture that these theories obey an OPE coefficient minimization principle. We then use this conjecture as well as the extremal functional method to reconstruct the first few low-lying scaling dimensions and OPE coefficients for both protected and unprotected multiplets that appear in the OPE of two stress tensor multiplets for all values of N. We also calculate the half and quarter-BPS operator OPE coefficients in the SU(2)k × SU(2)−k BLG theory for all values of the Chern-Simons coupling k, and show that generically they do not obey the same OPE coefficient minimization principle.

Beauty is Attractive: String-Theory, D-Branes, and Moduli Trapping at Enhanced Symmetry Points We study quantum effects on moduli dynamics arising from the production of particles which are light at points of enhanced symmetry in moduli space. The resulting forces trap the moduli at these points. Moduli trapping occurs in time-dependent quantum field theory, as well as in systems of moving D-branes, where it leads the branes to combine into stacks. Trapping also occurs in the presence of gravity, though the range over which the moduli can roll is limited by Hubble friction. We observe that a scalar field trapped on a steep potential can induce a stage of acceleration of the universe, which we call trapped inflation. Moduli trapping ameliorates the cosmological moduli problem and may affect vacuum selection. In particular, rolling moduli are most powerfully attracted to the points of greatest symmetry. Given suitable assumptions about the dynamics of the very early universe, this effect might help to explain why among the plethora of possible vacuum states of string theory, we appear to live in one with a large number of (spontaneously broken) symmetries.

The most comprehensive global fits to date of GUT-scale SUSY models with GAMBIT We present the most comprehensive global fits to date of three supersymmetric models motivated by grand unification: the Constrained Minimal Supersymmetric Standard Model (CMSSM), and its Non-Universal Higgs Mass generalisations NUHM1 and NUHM2. We include likelihoods from a number of direct and indirect dark matter searches, a large collection of electroweak precision and flavour observables, direct searches for supersymmetry at LEP and Runs I and II of the LHC, and constraints from Higgs observables. Our analysis improves on existing results not only in terms of the number of included observables, but also in the level of detail with which we treat them, our sampling techniques for scanning the parameter space, and our treatment of nuisance parameters. We show that stau co-annihilation is now ruled out in the CMSSM at more than 95% confidence. Stop co-annihilation turns out to be one of the most promising mechanisms for achieving an appropriate relic density of dark matter in all three models, whilst avoiding all other constraints. We find high-likelihood regions of parameter space featuring light stops and charginos, making them potentially detectable in the near future at the LHC. We also show that tonne-scale direct detection will play a largely complementary role, probing large parts of the remaining viable parameter space, including essentially all models with multi-TeV neutralinos.

On an integrable deformation of Kapustin-Witten systems In a celebrated work, Kapustin and Witten [1] described the geometric Langlands program (GLP) in terms of a compactification on a Riemann surface of a certain twisted version of the N = 4 superymmetric Yang-Mills theory (SYM) in four dimensions. In such paper, the authors introduced a set of equations after imposing a BRST-like preservation conditions on a twisted version of N = 4 SYM theory in four dimensions; these equations are now known as the Kapustin-Witten (KW) equations and have been the subject of an intensive work in the last decade in physics as well as in mathematics. In particular, a relation of KW equations with knot theory is also described by Witten in [2], where the author describes an approach to Khovanov homology using gauge theory; in that context, the KW equations appear as a localization condition of the N = 4 SYM theory in four dimensions (see [3] for a review on this topic). The KW equations are also closed related to another set of equations, recently introduced by Ward [4] and usually called the (2k)-Hitchin equations; it is important to mention that these equations are a natural generalization of another set of equations introduced by Hitchin [5] in a pionnering work in complex geometry; indeed, the article of Hitchin is the origin of the notion of Higgs bundle in mathematics, a notion that plays an important role in the physical interpretation of the GLP developed by Kapustin and Witten. In this article we study an integrable deformation of the Kapustin-Witten equations. Using the Weyl-Wigner-Moyal-Groenewold description an integrable ⋆-deformation of a Kapustin-Witten system is obtained. Starting from known solutions of the original equations, some solutions to these deformed equations are obtained.