Related papers: A Group-Theoretical Method for Natanzon Potentials…
Linear recursion relations for the instanton corrections to the effective prepotential of N=2 supersymmetric gauge theories with an arbitrary number of hypermultiplets in the fundamental representation of an arbitrary classical gauge group…
We present a unified formulation for higher gauge theory using generalized forms, encompassing higher connections, curvatures, and gauge transformations. We begin by developing the calculus of generalized forms valued in higher algebras and…
Using a superfield generalization of the tadpole method, we study the one-loop effective potential for a Wess Zumino model modified by a higher-derivative term, inspired by the Lee-Wick model. The one-loop K\"{a}hlerian potential is also…
We introduce new techniques for calculations in Gauge theories with extended supersymmetry. We are working in Projective Superspace where the $SU(2)$ R-symmetry is realized geometrically by including an auxilliary $\mathbb{CP}^1$ component…
This paper develops a theory of polynomial maps from commutative semigroups to arbitrary groups and proves that it has desirable formal properties when the target group is locally nilpotent. We apply this theory to solve Waring's Problem…
The renormalization group is used to improve the effective potential of massive ${\rm O}(N)$ symmetric $\phi^4$ theory. Explicit results are given at the two-loop level.
We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We show that, under those deformations, the logarithm of the…
We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…
A general procedure is presented how to improve the effective potential by using the renormalization group equation (RGE) in MS bar scheme. If one knows the L-loop effective potential and the RGE coefficient functions up to (L+1)-loop…
In this paper we compute gaugino and scalar condensates in N=1 supersymmetric gauge theories with and without massive adjoint matter, using localization formulae over the multi--instanton moduli space. Furthermore we compute the chiral ring…
In this paper, we define locally matchable subsets of a group which is derived from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…
The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite…
We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian…
We discuss integrating out matter fields and integrating in matter fields in four dimensional supersymmetric gauge theories. Highly nontrivial exact superpotentials can be easily obtained by starting from a known theory and integrating in…
In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of $G$-posets with $G$-equivariant coefficients. For this purpose, we need various local categories of a finite…
Explicit expressions for associated spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables. In this paper, we present explicit expressions for zonal functions of de Sitter…
The essential features of a full potential electronic structure method using Linear Muffin-Tin Orbitals (LMTOs) are presented. The electron density and potential in the this method are represented with no inherent geometrical approximation.…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources is study. In this context, effective potential are studied in order to understand the dynamics of the magnetic field in galaxies.…
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…