Non-commutative gauge theory of twisted D-branes

TL;DR

This paper introduces new non-commutative gauge theories for branes on twisted conjugacy classes, generalizing matrix models and providing classical solutions related to brane condensation.

Contribution

It proposes a novel class of non-commutative gauge theories based on microscopic solutions, extending fuzzy gauge theories to twisted conjugacy class branes.

Findings

Constructed classical solutions for the new gauge theories.

Interpreted solutions as brane condensation processes.

Generalized matrix models to curved backgrounds.

Abstract

In this work we propose new non-commutative gauge theories that describe the dynamics of branes localized along twisted conjugacy classes on group manifolds. Our proposal is based on a careful analysis of the exact microscopic solution and it generalizes the matrix models (`fuzzy gauge theories') that are used to study e.g. the bound state formation of point-like branes in a curved background. We also construct a large number of classical solutions and interpret them in terms of condensation processes on branes localized along twisted conjugacy classes.