Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States

TL;DR

This paper introduces a nonanticommutative deformation of ${\cal N}=4$ SYM theory, linking it to D3-branes in RR flux backgrounds, and explores its vacuum structure including fuzzy sphere configurations.

Contribution

It presents a novel deformation of ${\cal N}=4$ SYM theory via a star product, connecting it to Myers terms and D3-brane backgrounds with flux, and analyzes the resulting vacuum states.

Findings

Deformation introduces Myers-like bosonic terms.

Vacuum states include fuzzy two sphere configurations.

Existence of both supersymmetric and non-supersymmetric vacua.

Abstract

We propose a deformation of ${\cal N}=4$ SYM theoery induced by nonanticommutative star product. The deformation introduces new bosonic terms which we identify with the corresponding Myers terms of a stack of D3-branes in the presence of a five-form RR flux. We take this as an indication that the deformed lagrangian describes D3-branes in such a background. The vacuum states of the theory are also examined. In a specific case where the U(1) part of the gauge field is nonvanishing the (anti)holomorphic transverse coordinates of the brane sit on a fuzzy two sphere. For a supersymmetric vacuum the antiholomorphic coordinates must necessarily commute. However, we also encounter non-supersymmetric vacua for which the antiholomorphic coordinates do not commute.