U-duality and M-theory, an algebraic approach

TL;DR

This paper explores how U-duality in M-theory can be understood as an exact symmetry emerging from T-duality and 11D diffeomorphism invariance, using an algebraic framework involving Weyl groups and Borel generators.

Contribution

It provides an algebraic approach to derive U-duality groups from fundamental symmetries and discusses their implications for BPS states and duality-invariant mass formulas.

Findings

Weyl generators realize Weyl groups of SO(d,d,Z) and E_{d(d)}(Z)

Borel generators extend finite groups to full U-duality groups

Duality invariant mass formulas for BPS states derived

Abstract

Based on our work hep-th/9809039, we discuss how U-duality arises as an exact symmetry of M-theory from T-duality and 11D diffeomorphism invariance. A set of Weyl generators are shown to realize the Weyl group of SO(d,d,Z) and E_{d(d)}(Z), while Borel generators extend these finite groups into the full T- and U-duality groups. We discuss how the BPS states fall into various representations, and obtain duality invariant mass formulae, relevant for the computation of exact string amplitudes. The realization of U-duality symmetry in Matrix gauge theory is also considered.