Related papers: Mathematical structures behind supersymmetric dual…
In these notes, based on a talk given at the Rencontres de Moriond, I give a simple introduction to the tremendous progress that has been made during the last few years towards the understanding of strong-coupling phenomena in quantum gauge…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
The purpose of this article is to give an explicit description, in terms of hypergeometric functions over finite fields, of zeta function of a certain type of smooth hypersurfaces that generalizes Dwork family. The point here is that we…
When placed on four-manifolds, $ \mathcal{N} = 2 $ gauge theories couple to topological invariants of the background via two functions $ A $ and $ B $. General considerations allow for these functions to be fixed in terms of the Coulomb…
This theoretical review is intended to give non-theorists a flavor of the ideas driving the current efforts to experimentally find supersymmetry. We discuss the main reasons behind the expectation that supersymmetry may be "just around the…
We study possible relations between the full Green's functions of softly broken supersymmetric theories and the full Green's functions of rigid supersymmetric theories on the example of the supersymmetric quantum mechanics and find that…
The aim of this note is to establish an interesting hypergeometric generating relation contiguous to that of Exton by a short method.
A general criterion is given for the vanishing of the beta-functions in N=1 supersymmetric gauge theories.
We review a construction, using the harmonic space method, of solutions to the superfield equations of motion for N-extended self-dual supergravity theories. A superspace gauge condition suitable for the performance of a component analysis…
We calculate partition functions for supersymmetric heterotic theories on Melvin background with Wilson line. These functions coincide with partition functions for some of non-supersymmetric heterotic theories in appropriate limits. This…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
Results about the phase structure of certain N=1 supersymmetric gauge theories, which have been obtained as a consequence of holomorphy and `electric-magnetic' duality, are shown to be in quantitative agreement with corresponding…
We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N=2 supercharges are explicitly constructed in terms of differential forms. The analysis can be…
The purpose of my PhD thesis is to investigate different group theoretical and geometrical aspects of supergravity theories. To this aim, several research topics are explored: On one side, the construction of supergravity models in diverse…
Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geometry. Its objects of study include convex semialgebraic sets that arise in semidefinite programming and from sums of squares. This article…
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hypergeometric functions from the symmetries and other properties of…
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories…
We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve,…