Mass deformation of twisted super Yang-Mills theory with fuzzy sphere solution

TL;DR

This paper explores mass deformation of twisted super Yang-Mills theories across various models and dimensions, demonstrating the universal presence of fuzzy sphere solutions in their classical vacua.

Contribution

It systematically analyzes mass deformation methods in super Yang-Mills theories with four scalar supercharges, revealing the consistent emergence of fuzzy sphere solutions.

Findings

Multiple deformation methods identified for theories with four scalar supercharges.

Fuzzy sphere solutions found as classical vacua in all studied models.

Deformation approaches exclude the two-dimensional B-model.

Abstract

We investigate mass deformation of twisted superalgebra of U(N) super Yang-Mills (SYM) theories in several models and in several dimensions, motivated by the method formulated in [1]. We show that there are several ways to perform the deformation, if a model possesses four scalar supercharges except for two dimensional B-model. We also evaluate classical vacuum solutions of the potentials of scalar fields for each model. We then find that it is always possible to find fuzzy sphere solution in the theories.