NCOS and D-branes in Time-dependent Backgrounds

TL;DR

This paper explores noncommutative open string theories in time-dependent backgrounds, demonstrating how S-duality and SL(2,Z) transformations relate NCOS and NCYM theories with evolving noncommutativity parameters and providing their dual gravity descriptions.

Contribution

It introduces a framework for analyzing NCOS theories in time-dependent backgrounds and shows how dualities transform noncommutativity types and parameters over time.

Findings

S-duality maps NCYM with space-space noncommutativity to NCOS with time-dependent noncommutativity.

SL(2,Z) transformations generate NCOS with mixed noncommutativity in time-dependent settings.

Dual gravity descriptions are constructed for these time-dependent noncommutative theories.

Abstract

We study noncommutative open string (NCOS) theories realized in string theory with time-dependent backgrounds. Starting from a noncommutative Yang-Mills theory (NCYM) with a constant space-space noncommutativity but in a time-dependent background and making an S-dual transformation, we show that the resulting theory is an NCOS also in a time-dependent background but now with a time-dependent time-space noncommutativity and a time-dependent string scale. The corresponding dual gravity description is also given. A general SL(2,Z) transformation on the NCYM results in an NCOS with a time-dependent time-space noncommutativity and a constant space-space noncommutativity, and also in a time-dependent background.