Non-Commutative Moduli Spaces, Dielectric Tori and T-duality

TL;DR

This paper explores the use of non-commutative geometry to understand the moduli space of vacua in deformed N=4 super Yang-Mills theories, revealing topology changes and T-duality relations.

Contribution

It extends recent work by providing a worldsheet calculation that connects field theory results with non-commutative geometric interpretations of D-brane dynamics.

Findings

Different moduli space regions correspond to D5-branes with various topologies

Singularities indicate topology change in the moduli space

T-duality maps between mirror string realizations of the field theory

Abstract

We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet calculation that reproduces the field theory results and sheds some light on the dynamics of the D-brane bubbles. Different regions of moduli space are associated with D5-branes of various topologies; singularities in the moduli space are associated with topology change. T-duality on toroidal topologies maps between mirror string realizations of the field theory.