Twisted Bundle On Quantum Torus and BPS States in Matrix Theory

TL;DR

This paper explores twisted gauge bundles on quantum tori within M(atrix) theory, deriving BPS spectra that respect U-duality, advancing understanding of noncommutative geometry in string theory.

Contribution

It constructs twisted U(n) bundles on quantum tori as deformations of classical bundles and derives the BPS spectrum respecting full U-duality in M theory.

Findings

Constructed twisted U(n) bundles on quantum tori.

Derived BPS spectrum consistent with U-duality.

Connected noncommutative geometry with M-theory compactifications.

Abstract

Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider twisted gauge field configurations, we construct twisted U(n) bundles on the quantum torus as a deformation of its classical counterpart. By properly taking into account membranes winding around the light-cone direction, we derive from the M(atrix) model the BPS spectrum which respects the full SL(2,Z)*SL(2,Z) U-duality in M theory.