M-Theory and U-duality on T^d with Gauge Backgrounds

TL;DR

This paper explores the full U-duality symmetry in M-theory compactified on tori with gauge backgrounds, constructing an invariant mass formula and analyzing its implications for Matrix theory and BPS spectra.

Contribution

It introduces a U-duality invariant mass formula incorporating gauge backgrounds and interprets it within Matrix gauge theory, extending understanding of symmetries in M-theory.

Findings

Constructed an E_d(Z) invariant mass formula with gauge backgrounds.

Identified the coupling of the three-form as a topological theta term.

Demonstrated the action of E_{d+1}(Z) on BPS spectrum in Matrix theory.

Abstract

The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields. We construct an E_d(Z) U-duality invariant mass formula incorporating non-vanishing gauge backgrounds of the M-theory three-form C. We interpret this mass formula from the point of view of the Matrix gauge theory, and identify the coupling of the three-form to the gauge theory as a topological theta term, in agreement with earlier conjectures. We give a derivation of this fact from D-brane analysis, and obtain the Matrix gauge theory description of other gauge backgrounds allowed by the Discrete Light-Cone Quantization. We further show that the conjectured extended U-duality symmetry of Matrix theory on T^d in the Discrete Light-Cone Quantization has an implementation as an action of E_{d+1}(Z) on the BPS spectrum. Some implications for the proper interpretation of the rank N of the Matrix gauge theory are discussed.