T-duality of non-commutative gauge theories

TL;DR

This paper explores the T-duality relationships between different gauge theories on D-branes, demonstrating their equivalence through D1-brane configurations and connecting these dualities to Morita equivalence.

Contribution

It introduces a dual D1-brane perspective for a continuous set of equivalent gauge theories and clarifies the parameter relations via brane rotations.

Findings

Dual D1-brane configurations reproduce parameter relations.

The duality relates to Morita equivalence.

Equivalence extends to a continuous set of gauge theories.

Abstract

Via T-duality a theory of open strings on a D1-brane wrapped along a cycle of slanted torus is described by a U(1) gauge theory on a D2-brane in the B-field background. It is also known that there is another dual description of the D1-brane configuration by a non-commutative gauge theory on a D2-brane. Therefore, these two gauge theories on D2-branes are equivalent. Recently, the existence of a continuous set of equivalent gauge theories including these two was suggested. We give a dual D1-brane configuration for each theory in this set, and show that the relation among parameters for equivalent gauge theories can be easily reproduced by rotation of the D1-brane configuration. We also discuss a relation between this duality and Morita equivalence.