Super Yang-Mills Theories with Inhomogeneous Mass Deformations

TL;DR

This paper constructs inhomogeneously mass-deformed super Yang-Mills theories from known models, analyzes their supersymmetric vacua, and explores solutions with constant and periodic mass functions, linking them to type IIB supergravity.

Contribution

It introduces new inhomogeneous mass-deformed super Yang-Mills theories derived from ${ m N}=1^*$ and ${ m N}=2^*$ models and analyzes their supersymmetric vacua and solutions.

Findings

Derived explicit vacuum solutions for constant and periodic mass functions.

Established boundary conditions relating vacua parameters at asymptotic boundaries.

Connected vacuum solutions to brane configurations in type IIB supergravity.

Abstract

We construct the 4-dimensional ${\cal N}=\frac12$ and ${\cal N}=1$ inhomogeneously mass-deformed super Yang-Mills theories from the ${\cal N} =1^*$ and ${\cal N} =2^*$ theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the ${\cal N} =4$ super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $ {\cal N}=\frac12$ theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.