Related papers: Unified Theories from Fuzzy Extra Dimensions
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field…
Higher-dimensional theories provide a promising framework for unified extensions of the supersymmetric standard model. Compactifications to four dimensions often lead to U(1) symmetries beyond the standard model gauge group, whose breaking…
We analyze the possibility to construct a self-consistent gauge field theory in $D>4$. We first look for the cancellation of the UV divergences in SUSY theories. Then, following the Wilson RG approach, we study the RG equation for the gauge…
We study the unitarity of the standard model (SM) in higher dimensions. We show that the essential features of SM unitarity remain after compactification, and place bounds on the highest Kaluza-Klein (KK) level N_KK and the Higgs mass m_H…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
The low-energy physics of systems with spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It has been known for half a century how to construct invariant Lagrangian densities for the low-energy…
We analyze the class of four-dimensional N = 4 supergravities obtained by gauging the axionic shift and axionic rescaling symmetries. These theories are formulated with the machinery of embedding tensors and shown to be deducible from…
Spacetimes obtained by dimensional reduction along lattices containing a lightlike direction can admit semigroup extensions of their isometry groups. We show by concrete examples that such a semigroup can exhibit a natural order, which in…
Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…
Scalar fields are studied on fuzzy $S^4$ and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4 in the fuzzy…
We investigate the coset structures which appear in the dimensional reduction of supergravity theories. Especially we investigate how to recognize the global symmetry groups if the coset is non-split. As an example we apply our analysis to…
We study $SO(m)$ covariant Matrix realizations of $ \sum_{i=1}^{m} X_i^2 = 1 $ for even $m$ as candidate fuzzy odd spheres following hep-th/0101001. As for the fuzzy four sphere, these Matrix algebras contain more degrees of freedom than…
We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the geometry associated with several types of singularities…
Within the gauge-theoretic approach of gravity, the gauging of an enlarged symmetry of the tangent space in four dimensions allows gravity to be unified with internal interactions. We study the unification of the Conformal and…
We review the mathematical tools required to cull and filter representations of the Coxeter Group $BC_4$ into providing bases for the construction of minimal off-shell representations of the 4D, $ {\cal N}$ = 1 spacetime supersymmetry…
We study compactifications on Riemann surfaces with punctures of N=(1,0) 6d SCFTs with a one dimensional tensor branch and no continuous global symmetries. The effective description of such models on the tensor branch is in terms of pure…
In these notes we review Klimcik's construction of noncommutative gauge theory on the fuzzy supersphere. This theory has an exact SUSY gauge symmetry with a finite number of degrees of freedom and thus in principle it is amenable to the…
A gauge theory of gravity is defined in 6 dimensional non-commutative space-time. The gauge group is the unitary group U(2,2), which contains the homogeneous Lorentz group, SO(4,2), in 6 dimensions as a subgroup. It is shown that, after the…
Over the last 25 years, the notion of "fuzzy spaces" has become ubiquitous in the high-energy physics literature. These are finite dimensional noncommutative approximations of the algebra of functions on a classical space. The most well…