Aspects of the T-duality construction for the Supermembrane theory

TL;DR

This paper explores how T-duality symmetry in supermembrane theory compactified on M9xT2 reduces to a specific subgroup of SL(2,Z), aiding understanding of dualities in nine-dimensional supergravity.

Contribution

It explicitly demonstrates the reduction of T-duality to a parabolic subgroup of SL(2,Z) in supermembrane theory, linking it to nine-dimensional gauged supergravity.

Findings

T-duality reduces to a parabolic subgroup of SL(2,Z)

Non-linear action on moduli and charges

Connection to nine-dimensional gauged supergravity

Abstract

In this note we explicitly show how the generalization of the T-duality symmetry of the supermembrane theory compactified in M9xT2 can be reduced to a parabolic subgroup of SL(2,Z) that acts non-linearly on the moduli parameters and on the KK and winding charges of the supermembrane. This is a first step towards a deeper understanding of the dual relation between the parabolic type II gauged supergravity in nine dimensions.