Recent Results on N=2,4 Supersymmetry with Lorentz Symmetry Violating

We construct a collection of Lorentz violating Yang-Mills theories exhibiting supersymmetry.

Some notions in non-perturbative dynamics of supersymmetric gauge theories are being reviewed. This is done by touring through a few examples.

In this paper, we present and classify the supersymmetric extensions of extended kinematical algebras, at the basis of non-Lorentzian physics theories. The diverse kinematical superalgebras are here derived by applying non- and ultra-relativistic expansion procedures involving different semigroups. We then build three-dimensional Chern-Simons non-Lorentzian supergravity theories based on such (extended) kinematical superalgebras, providing the supersymmetry transformation law...

The topic of 4D, N = 1 supersymmetry is introduced for the reader with a prior background in relativistic quantum field theory. The presentation is designed to be a useful primer for those who plan to later engage in serious investigation of the area or as an overview for the generally interested.

In this paper, we take up an old thread of development concerning the characterization of supersymmetric theories without any use of anticommuting variables that goes back to one of the authors' very early work [1]. Our special focus here will be on the formulation of supersymmetric Yang-Mills theories, extending previous results beyond $D=4$ dimensions. This perspective is likely to provide new insights into these theories, and in particular the maximally extended $N=4$ theo...

In this paper we consider the problem of spontaneous supersymmetry breaking in $N=4$ supergravity interacting with vector multiplets. We start with the ordinary version of such model with the scalar field geometry $SU(1,1)/U(1)\otimes SO(6,m)/SO(6)\otimes SO(m)$. Then we construct a dual version of this theory with the same scalar field geometry, which corresponds to the interaction of arbitrary number of vector multiplets with the hidden sector, admitting spontaneous supersy...

This is a brief survey of applications of the harmonic superspace methods to the models of N=4 supersymmetric quantum mechanics (SQM). The main focus is on a recent progress in constructing SQM models with couplings to the background non-Abelian gauge fields. Besides reviewing and systemizing the relevant results, we present some new examples and make clarifying comments.

An introduction to and a partial review of supergravity theories is given, insisting on concepts and on some important technical aspects. Topics covered include elements of global supersymmetry, a derivation of the simplest N=1 supergravity theory, a discussion of N=1 matter-supergravity couplings, of the scalar sector and of some simple models. Space-time is four-dimensional.

In these lectures we discuss various aspects of gauge theories with extended $N=2$ and $N=4$ supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action for the light degrees of freedom in the $N=2$ super Yang-Mills theory and the conjecture, supported by some checks, that the $N=4$ super Yang-Mills theory is dual in the sense of Montonen-Olive.

Some recent results in supersymmetric grand unified theories are reviewed.