We investigate Seiberg’s N = 1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in Type IIA string theory is gi...

The massive SU (2) gauge field theory coupled with fermions is considered in 2 + 1 dimensions. Quark energy spectrum and radiative shift in constant external nonabelian field, being exact solution of the gauge field equations with the Chern-Simons term, are calculated. Under the condition m = θ/4 the quark state is shown to be supersymmetric.

Supersymmetry (SUSY), introduced in theoretical physics and mathematics, has a lot of interesting applications [1]. One of them consists in mixing fermionic and bosonic states. It has important consequences in the quantum field theory, namely, this property provides a mechanism for cancellation of the ultraviolet divergences. Moreover, supersymmetric quantum field theory (SSQT) allows to unify ...

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis...

The numerical simulation we report on aims at a better understanding of the non-perturbative low-energy features of supersymmetric gauge theories. We concentrate on the simplest supersymmetric gauge theory, namely SU(2),N = 1 superYang-Mills. This model contains, in addition to the gauge field a massless Majorana fermion in the adjoint representation (called gluino). For the theoretical motivat...

I review motivations for the study of supersymmetric field theories by lattice techniques. In particular, some of the more interesting potential applications are described. These are models of quantum gravity, that rely on the AdS/CFT correspondence. The dual gauge theory is an ideal place for lattice studies to make a contribution. I also survey some of the recent advances in lattice formulati...

The only string models known to reproduce the Minimal Supersymmetric Standard Model in the low energy effective field theory are those constructed in the free fermionic formulation. We demonstrate the existence of quasi– realistic free fermionic heterotic–string models in which supersymmetric singlet flat directions do not exist. This raises the possibility that supersymmetry is broken perturba...

We present a model for supersymmetric Yang-Mills theory in 10+2 dimensions. Our construction uses a constant null vector, and leads to a consistent set of field equations and constraints. The model is invariant under generalized translations and an extra gauge transformation. Ordinary dimensional reduction to ten dimensions yields the usual supersymmetric Yang-Mills equations, while dimensional...

We consider the gauged N = 2 (simple) supersymmetric seven-dimensional ( d = 7 ) supergravity theory with the scalar field potential having two critical points. Applying a modified Witten argument reduces the question of stability to deciding if a particular non-linear ordinary differential equation has a global solution. We show that it does and that therefore the non-supersymmetric ground sta...

I review motivations for the study of supersymmetric field theories by lattice techniques. In particular, some of the more interesting potential applications are described. These are models of quantum gravity, that rely on the AdS/CFT correspondence. The dual gauge theory is an ideal place for lattice studies to make a contribution. I also survey some of the recent advances in lattice formulati...