Related papers: Finiteness in N=1 SYM Theories

We develop a systematic approach to confinement in N=1 supersymmetric theories. We identify simple necessary conditions for theories to confine without chiral symmetry breaking and to generate a superpotential non-perturbatively…

We show that the category of symmetric spectra can be used as a model for global equivariant homotopy theory of finite groups.

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite…

Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…

Supersymmetry is a prominent candidate for physics beyond the standard model. In order to compute the spectrum of supersymmetric theories, we employ nonperturbative lattice QFT techniques which due to the discretisation of spacetime violate…

We study $\mathcal{N}=1$ supersymmetric Yang-Mills theory (SYM) on the lattice. The non-perturbative nature of supersymmetric field theories is still largely unknown. Similarly to QCD, SYM is confining and contains strongly bound states.…

We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.

It is shown that finite groups in which the order of the product of every pair of elements of co-prime order is the product of the orders, is nilpotent.

We give a classification and overview of the confining N=1 supersymmetric gauge theories. For simplicity we consider only theories based on simple gauge groups and no tree-level superpotential. Classification of these theories can be done…

We formulate four-dimensional N=2 supersymmetric nonlinear sigma models in N=1 superspace. We show how to add superpotentials consistent with N=2 supersymmetry. We lift our construction to higher-dimensional spacetime and write…

A translation of Emmy Noether's paper "Der Endlichkeitsatz der Invarianten endlicher Gruppen" (Mathematische Annalen, vol. 77, 1920, pages 89--92). In Noether's words, the paper gives "an entirely elementary finiteness proof---using only…

We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse…

In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations.…

We revisit the issue of higher-dimensional counterterms for the N=(1,1) supersymmetric Yang-Mills (SYM) theory in six dimensions using the off-shell N=(1,0) and on-shell N=(1,1) harmonic superspace approaches. The second approach is…

We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give…

In this paper, we consider the simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices.

In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.

We discuss the ways of constructing the exact superpotential for N=1 supersymmetric theories and propose a new approach. As a consequence, a new structure of the superpotential is found.

Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…