T-duality Invariance of the Supermembrane

TL;DR

This paper demonstrates that supermembrane theory compactified on a torus exhibits T-duality invariance, revealing new topological sectors and connecting to string theory dualities.

Contribution

It explicitly constructs the T-duality transformation for supermembranes and interprets it globally via bundle theory, extending string T-duality to M2-branes.

Findings

T-duality is an exact symmetry of the supermembrane theory.

The T-duality transformation acts locally and has a global bundle interpretation.

In the string limit, supermembrane T-duality reduces to known string T-duality and reveals SL(2,Z) multiplets.

Abstract

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second cohomology class. We find the explicit T-duality transformation that acts locally on the supermembrane theory and we show that it is an exact symmetry of the theory. We give a global interpretation of the T-duality in terms of bundles. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. We show that in the limit when the torus degenerate into a circle and the M2 mass operator restricts to the string-like configurations, the usual closed string T-duality transformation between the type IIA and type IIB mass operators is recovered. Moreover if we just restrict M2 mass operator to string-like configurations but we perform a generalized T-duality we find the SL(2,Z) non-perturbative multiplet of IIA.