T-Duality and Ramond-Ramond Backgrounds in the Matrix Model

TL;DR

This work addresses how T-duality acts on the DLCQ Matrix Model for toroidally compactified M-theory in the presence of Ramond-Ramond backgrounds. It treats the compactified Matrix model as a noncommutative SYM theory on the dual torus with deformation parameter $\Theta$ induced by the NS-NS $B$-field and extends this duality to RR moduli by encoding RR data into a chiral spinor $\chi$ transforming under $SO(3,3|Z)$ via $\bar{\chi}=S(\Lambda)\chi$. The main contributions are the explicit transformation laws for RR moduli derived from the 7D Type IIA reduction, and the demonstration that Chern–Simons-type terms in the noncommutative gauge theory transform consistently under duality, yielding an invariant action under $SO(3,3|Z)$ with $\bar{A}_{(0)}$ and $(\bar{u}-\bar{\Theta}\bar{v})$ obeying precise relations. This work therefore provides a duality-covariant framework linking noncommutative gauge theory data to Ramond-Ramond moduli in string theory, with implications for the spectrum and consistency of Matrix-model compactifications.

Abstract

We investigate T-duality of toroidally compactified Matrix model with arbitrary Ramond-Ramond backgrounds in the framework of noncommutative super Yang-Mills gauge theory.