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The existence of an extremal self-dual binary linear code C of length 72 is a long-standing open problem. We continue the investigation of its automorphism group: looking at the combination of the subcodes fixed by different involutions and…

Given a finite group $G$ and positive integers $r$ and $s$, a problem of interest in algebra is determining the minimum cardinality of the product set $AB$, where $A$ and $B$ are subsets of $G$ such that $|A|=r$ and $|B|=s$. This problem…

In this paper, we study the problems of abelian group isomorphism and basis construction in two models. In the {\it partially specified model} (PS-model), the algorithm does not know the group size but can access randomly chosen elements of…

Within the framework of "anomalously gauged" Wess-Zumino-Witten (WZW) models, we construct solutions which include nonabelian fields. Both compact and noncompact groups are discussed. In the case of compact groups, as an example of…

We discuss type IIB orientifolds with D-branes, and NSNS and RR field strength fluxes, with D-brane sectors leading to open string spectra with non-abelian gauge symmetry and charged chiral fermions. The closed string field strengths…

The restrictions imposed by anomaly cancellation on the chiral fermion content of nonsupersymmetric gauge theories based on various groups are studied in spacetime dimension D=6, 8, and 10. In particular, we show that the only…

We extend the string model building rules for the construction of chiral supersymmetric Type I compactifications on smooth Calabi-Yau manifolds. These models contain stacks of D9-branes endowed with general stable U(n) bundles on their…

We consider a 5-dimensional SU(5) model wherein the symmetry is broken to the 4-dimensional Standard Model by compactification of the 5th dimension on an S^1/(Z_2 \times Z^\prime_2) orbifold. We identify the members of all SU(5)…

We say that a countable discrete group $\Gamma$ satisfies the invariant von Neumann subalgebras rigidity (ISR) property if every $\Gamma$- invariant von Neumann subalgebra $\mathcal{M}$ in $L(\Gamma)$ is of the form $L(\Lambda)$ for some…

We construct chiral N=1 gauge theories in 4D by compactifying the 6D Blum-Intriligator (1,0) theories of 5-branes at $A_k$ singularities on $T^2$ with a nontrivial bundle of the global U(1) symmetry of these theories.

We classify the large $N$ limits of four-dimensional supersymmetric gauge theories with simple gauge groups that flow to superconformal fixed points. We restrict ourselves to the ones without a superpotential and with a fixed flavor…

I consider the construction of heterotic orbifold models based on a toroidal orbifold with non Abelian point group. I construct an explicit model based on the point group $S_3$ and calculate the spectrum and remnant symmetries. This model…

The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified Kaluza-Klein type approach in which the internal space…

The strategy for assigning $Z_{4R}$ parity in the string compactification is presented. For the visible sector, an anti-SU(5) (flipped-SU(5)) grand unification (GUT) model with three families is used to reduce the number of representations…

We study topologically stable defect structures in systems where the defect line classification in three dimensions and associated algebra of interactions (the fundamental group) are governed by the non-Abelian 8-element group, the…

Let $k$ be a number field and $B$ be a central simple algebra over $k$ of dimension $p^2$ where $p$ is prime. In the case that $p=2$ we assume that $B$ is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal…

We derive the Standard model gauge group together with chiral fermion generations from the heterotic string by turning on a Wilson line on a non-simply connected Calabi-Yau threefold with an SU(5) gauge group. For this we construct stable…

Let $\mathfrak{A}$ be a finite abelian group. In this article, we classify harmonic $\mathfrak{A}$-covers of a tropical curve $\Gamma$ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined…

Given a finite group $G$, we say that $G$ has weak normal covering number $\gamma_w(G)$ if $\gamma_w(G)$ is the smallest integer with $G$ admitting proper subgroups $H_1,\ldots,H_{\gamma_w(G)}$ such that each element of $G$ has a conjugate…

We will compute the stable upper genus for the family of finite non-abelian simple groups $PSL_2(\mathbb{F}_p)$ for $p \equiv 3~(mod~4)$. This classification is well-grounded in the other branches of Mathematics like topology, smooth, and…