Related papers: Mathematical structures behind supersymmetric dual…
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality…
Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An…
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
We review our efforts in investigating gauge theories with fermions in the adjoint representation of the gauge group by means of numerical simulations. These theories have applications in possible extensions of the Standard Model of…
Survey of hypergeometric motives, with a focus on their source varieties, Hodge numbers, and L-functions.
We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.
Under the assumption that all the gauge groups in supersymmetric theories unify at the fundamental scale, the numbers and the mass scales of messenger quarks and leptons, as well as the beta-function coefficient of the sector for dynamical…
We review electric/magnetic duality in $N=4$ (and certain $N=2$) globally supersymmetric gauge theories and show how this duality, which relates strong to weak coupling, follows as a consequence of a string/string duality. Black holes,…
This is an elementary introduction to basic tools of supersymmetry: the spacetime symmetries, gauge theory and its application in gravity, spinors and superalgebras. Special attention is devoted to conformal and anti-de Sitter algebras.
Gravity mediated supersymmetry breakdown originated from a study of gaugino condensation in a hidden sector. We review this mechanism of supergravity breakdown from the original formulation in the early eighties to its natural…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
This paper is an attempt to apply the tools of supergeometry to arithmetic. Supergeometric objects are defined over supercommutative rings of coefficients, and we consider an integral ring with exactly two odd variables. In this case the…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
Equivalence of partition functions for U(1) gauge theory and its dual in appropriate phase spaces is established in terms of constrained hamiltonian formalism of their parent action. Relations between the electric--magnetic duality…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
We re-examine perturbative and nonperturbative aspects of the beta function in N=1 and N=2 supersymmetric gauge theories, make comments on the recent literature on the subject and discuss the exactness of several known results such as the…
We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic…