Can global internal and spacetime symmetries be connected without supersymmetry?

Can global internal and spacetime symmetries be connected without supersymmetry? To answer this question,
we investigate Minkowski spacetimes with d space-like extra dimensions and point out under which general
conditions external symmetries induce internal symmetries in the effective 4-dimensional theories. We further
discuss in this context how internal degrees of freedom and spacetime symmetries can mix without supersymmetry
in agreement with the Coleman-Mandula theorem. We present some specific examples which rely on a
direct product structure of spacetime such that orthogonal extra dimensions can have symmetries which mix
with global internal symmetries. This mechanism opens up new opportunities to understand global symmetries
in particle physics. The nature of spacetime is still a great mystery in fundamental
physics and it might be a truly fundamental quantity
or it could be an emergent concept. An appealing and most
minimalistic approach would be if spacetime and propagating
degrees of freedom would have a common origin on equal
footing. In such a scenario, spacetime is thus an emergent
quantity and there seems to be no reason for it to be restricted
to a 4-dimensional Poincar´e symmetry apart from low energy
phenomenology. The only exception are additional time-like
dimensions which typically lead to inconsistencies when requiring
causality [1, 2], while there is no consistency problem
with additional space-like dimensions. Additional space-like
dimensions have therefore been widely studied.
If spacetime and particles consist of the same building
blocks, then a fundamental connection of these low energy
quantities should exist at high energies. Early attempts in
this direction have lead to the Coleman-Mandula no-go theorem
[3]. The no-go theorem shows under general assumptions
that a symmetry group accounting for 4-dimensional
Minkowski spacetime and internal symmetries has to factor
into the direct product of spacetime and internal symmetries.
This implies that spacetime and particle symmetries cannot
mix in relativistic interacting theories.
One way to circumvent the no-go theorem is to study
graded symmetry algebras which introduce fermionic symmetry
generators and are known as supersymmetries [4]. The
possibility to mix spacetime and internal symmetries in a relativistic
theory is a strong theoretical argument for supersymmetry
and supersymmetric extensions of the Standard Model
of particle physics are therefore widely studied. However,
there is no experimental evidence for supersymmetry, see
e.g. [5–7], and it is a finely question to ask: Are there alternative
ways to circumvent the Coleman-Mandula theorem?