Holography and D3-branes in Melvin Universes

TL;DR

This paper explores the formulation and dualities of space-dependent noncommutative super Yang-Mills and open string theories in Melvin universes, revealing their thermodynamics and connections to light-like noncommutative theories.

Contribution

It demonstrates how S-duality transforms NCSYM into NCOS with space-dependent noncommutativity and analyzes their thermodynamics and relation to light-like theories via Lorentz boosts.

Findings

Space-dependent NCSYM and NCOS share thermodynamics with constant noncommutative theories.

S-duality maps NCSYM to NCOS with both space-space and space-time noncommutativity.

Lorentz boosts on D3-branes lead to light-like NCSYM with space-dependent noncommutativity.

Abstract

Recently,in a paper hep-th/0511197, it was found that non-commutative super Yang-Mills (NCSYM) theory with space-dependent noncommutativity can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe supported by a flux of the NSNS B-field. Under S-duality, we show that this theory turns into a noncommutative open string (NCOS) theory with space-dependent space-time noncommutativity and effective space-dependent string scale. It is an NCOS theory with both space-dependent space-space and space-time noncommutativities under more general $SL(2,\mathbb{Z})$ transformation. These space-dependent noncommutative theories (NCSYM and NCOS) have completely the same thermodynamics as that of ordinary super YM theory, NCSYM and NCOS theories with constant noncommutativity in the dual supergravity description. Starting from black D3-brane solution in the Melvin universe and making a Lorentz boost along one of spatial directions on the worldvolume of D3-branes, we show that the decoupled theory is a light-like NCSYM theory with space-dependent noncommutativity in a static frame or in an infinite-momentum frame depending on whether there is a gravitational pp-wave on the worldvolume of the D3-branes.