SL(2,Z) symmetries, Supermembranes and Symplectic Torus Bundles

TL;DR

This paper formulates the 11D supermembrane as a symplectic torus bundle with SL(2,Z) symmetries, revealing dualities and suggesting origins of gauged effective theories in M-theory.

Contribution

It provides an explicit construction of supermembranes as symplectic torus bundles with monodromy, classifying their SL(2,Z) symmetries and implications for M-theory.

Findings

Supermembrane modeled as symplectic torus bundle with monodromy

Explicit classification of SL(2,Z) duality symmetries

Insights into the origin of gauged theories in M-theory

Abstract

We give the explicit formulation of the 11D supermembrane as a symplectic torus bundle with non trivial monodromy and non vanishing Euler class. This construction allows a classification of all supermembranes showing explicitly the discrete SL(2,Z) symmetries associated to dualities. It hints as the origin in M-theory of the gauging of the effective theories associated to string theories.