T-duality in M-theory and supermembranes

TL;DR

This paper explores T-duality in M-theory and supermembranes, showing how different representations relate and deriving a discrete mass spectrum in unstable regions, connecting string bound states and membrane spectra.

Contribution

It demonstrates the equivalence of two T-dual representations of supermembranes in M-theory and derives a discrete mass spectrum in unstable regimes.

Findings

BPS mass formulas agree in dual descriptions.

Reproduction of the BPS mass spectrum of (q1,q2) strings.

Derivation of a discrete mass spectrum in unstable membrane regions.

Abstract

The (q_1,q_2) SL(2,Z) string bound states of type IIB superstring theory admit two inequivalent (T-dual) representations in eleven dimensions in terms of a fundamental 2-brane. In both cases, the spectrum of membrane oscillations can be determined exactly in the limit $g^2\to \infty $, where $g^2$ is the type IIA string coupling. We find that the BPS mass formulas agree, and reproduce the BPS mass spectrum of the $(q_1,q_2)$ string bound state. In the non-BPS sector, the respective mass formulas apply in different corners of the moduli space. The axiomatic requirement of T-duality in M-theory permits to derive a discrete mass spectrum in a (thin torus) region where standard supermembrane theory undergoes instabilities.