Dualities, Twists, and Gauge Theories with Non-Constant Non-Commutativity

TL;DR

This paper explores non-commutative gauge theories arising from D3-branes in Melvin backgrounds with non-constant non-commutativity, providing a unified perspective on various known models and analyzing decay processes.

Contribution

It introduces a unified framework for understanding non-commutative gauge theories from D-branes in Melvin universes with non-constant non-commutativity, connecting different twist constructions.

Findings

Identifies the open string dynamics as non-commutative gauge theory with non-constant non-commutativity.

Unifies various Melvin twist models of D3-branes as special cases.

Describes decay of the D3-brane world volume via monopole pair nucleation.

Abstract

We study the world volume theory of D3-branes wrapping the Melvin universe supported by background NSNS B-field. In the appropriate decoupling limit, the open string dynamics is that of non-commutative guage field theory with non-constant non-commutativity. We identify this model as a simple Melvin twist of flat D3 branes. Along similar lines, one recognizes the model of Hashimoto and Sethi as being the Melvin null twist, and the model of Dolan and Nappi as being the null Melvin twist, of the flat D3-brane. This construction therefore offers a unified perspective on most of the known explicit constructions of non-commutative gauge theories as a decoupled theory of D-branes in a B-field background. We also describe the world volume theory on the D3-brane in Melvin universe which is decaying via the nucleation of monopole anti-monopole pair.