Deformation of Super Yang-Mills Theories in R-R 3-form Background

TL;DR

This paper investigates how constant R-R 3-form backgrounds deform N=2 and N=4 super Yang-Mills theories, revealing supersymmetry breaking patterns, classical vacua structures, and reformulations in superspace.

Contribution

It provides explicit calculations of the deformed Lagrangians from string amplitudes and analyzes supersymmetry and vacuum structures in the presence of R-R backgrounds.

Findings

Supersymmetry is fully broken in N=4 case for generic deformation.

Classical vacua include fuzzy sphere configurations.

Deformations can be interpreted as modifications of coupling constants in N=1 superspace.

Abstract

We study deformation of N=2 and N=4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at the second order in the deformation parameter from open string disk amplitudes. In N=4 case we find that all supersymmetries are broken for generic deformation parameter but part of supersymmetries are unbroken for special case. We also find that classical vacua admit fuzzy sphere configuration. In N=2 case we determine the deformed supersymmetries. We rewrite the deformed Lagrangians in terms of N=1 superspace, where the deformation is interpreted as that of coupling constants.