Related papers: $SU(n)$ symmetry breaking by rank three and rank t…
If an extra supersymmetric U(1) gauge factor exists at the TeV energy scale, which is then broken together with the supersymmetry, there will be several interesting and important phenomenological consequences, not only at the TeV scale, but…
It is shown that supersymmetry is spontaneously broken in certain three-dimensional supersymmetric gauge theories, by using the s-rule in their string theory realization as brane configurations. In particular, supersymmetry is broken in N=3…
The tensor rank decomposition is a useful tool for the geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able…
We develop a systematic way to solve linear equations involving tensors of arbitrary rank. We start off with the case of a rank $3$ tensor, which appears in many applications, and after finding the condition for a unique solution we derive…
We construct a supersymmetric grand unified model in the framework of a latticized extra dimension. The SU(5) symmetries on the lattice are broken by the vacuum expectation values of the link fields connecting adjacent SU(5) sites, leaving…
We prove a lower bound on the rank of tensors constructed from families of linear maps that `expand' the dimension of every subspace. Such families, called {\em dimension expanders} have been studied for many years with several known…
Duality symmetries are discussed for non-linear gauge theories of (n-1)-th rank antisymmetric tensor fields in general even dimensions d=2n. When there are M field strengths and no scalar fields, the duality symmetry groups should be…
The s-confining theories are a class of supersymmetric gauge theories with infrared dynamics which are well-understood. Perturbing such theories can give rise to dynamical supersymmetry breaking. We realize simple models of dynamical…
We propose a realistic theory based on the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes SU(3)_R \otimes U(1)_{X}}$ gauge group which requires the number of families to match the number of colors. In the simplest realization neutrino masses…
We examine the supersymmetric non-linear O(N) sigma model with a soft breaking term. In two dimensions, we found that the mass difference between supersymmetric partner fields vanishes accidentally. In three dimensions, the mass difference…
We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d $E_1$ and $\tilde{E}_1$ theories. Some of the resulting IR phases are described by IR free supersymmetric…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
The appearance of a broken supersymmetric U(1) gauge factor at the TeV scale is relevant for several reasons. If it truly exists, then one important consequence is that at the 100 GeV energy scale, the two-doublet Higgs structure is of a…
We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N-1 monopoles with minimal symmetry breaking. Using this we construct families of tetrahedrally symmetric SU(4) and…
We build a supersymmetric version with $SU(3)_C\otimes SU(2)_L\otimes U(1)_{Y^\prime}\otimes U(1)_{B-L}$ gauge symmetry, where $Y^\prime$ is a new charge and $B$ and $L$ are the usual baryonic and leptonic numbers. The model has three…
We introduce various notions of rank for a symmetric tensor, namely: rank, border rank, catalecticant rank, generalized rank, scheme length, border scheme length, extension rank and smoothable rank. We analyze the stratification induced by…
There are several advantages of introducing adjoint superfields at intermediate energies around $M=10^{13}$ GeV. Such as (i) gauge couplings still unify (ii) neutrino masses and mixings are produced (iii) primordial lepton asymmetry can be…
In string theory, higher rank antisymmetric tensor fields appear as massless excitations of closed strings. Till date there is no experimental support in favour of their existence. In a stringy framework, starting from a warped throat-like…
Finding the rank of a tensor is a problem that has many applications. Unfortunately it is often very difficult to determine the rank of a given tensor. Inspired by the heuristics of convex relaxation, we consider the nuclear norm instead of…
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…