The Galilean Nature of V-duality for Noncommutative Open String and Yang-Mills Theories

TL;DR

This paper investigates the V-duality conjecture for noncommutative open string and Yang-Mills theories, demonstrating that it corresponds to Galilean boosts in the gravity dual framework and that certain physical properties remain invariant under this duality.

Contribution

It provides a gravity dual analysis confirming that V-duality corresponds to Galilean boosts and shows invariance of the running string tension under this duality.

Findings

V-duality relates NCOS and NCYM theories via Galilean boosts.

Decoupled NCOS only permits infinitesimal Lorentz boosts.

The running string tension remains unchanged under V-duality.

Abstract

A V-duality conjecture for noncommutative open string theories (NCOS) that result from decoupling D-branes in Lorentz-boost related backgrounds was put forward recently in hep-th/0006013. The aim of this paper is to test the Galilean nature of this conjecture in the gravity dual setup. We start with an (F, D3) bound state Lorentz-boosted along one D3-brane direction perpendicular to the F-string, and show that insisting a decoupled NCOS allows only infinitesimal Lorentz boosts. In this way, it is shown that the V-duality relates a family of NCOS by Galileo boosts. Starting with a Lorentz-boosted (D1,D3) bound state, we show that a similar V-duality works for noncommutative Yang-Mills (NCYM) theories as well. In addition, we deduce by a holography argument that the running string tension, as a function of the energy scale, for NCOS (or NCYM) remains unchanged under V-duality.