Supersymmetric algebra of the massive supermembrane

TL;DR

This paper derives the explicit supersymmetric algebra for a massive supermembrane, exploring its formulation as a limit of a supermembrane on a genus-two surface and analyzing its symmetries and surface terms.

Contribution

It provides the explicit supersymmetric algebra including surface terms for the massive supermembrane and formulates it as a limit of a supermembrane on a genus-two surface.

Findings

Explicit expression of the supersymmetric algebra with surface terms

Formulation as a limit of supermembrane on a genus-two surface

Identification of preserved symmetries, including parabolic SL(2,Z)

Abstract

In this paper, we obtain the explicit expression of the supersymmetric algebra associated with the recently proposed massive supermembrane including all surface terms. We formulate the theory as the limit of a supermembrane on a genus-two compact Riemann surface when one of the handles becomes a string attached to a torus. The formulation reduces to a supermembrane on a punctured torus with a "string spike" (in the sense of \cite{dwln}), attached to it. In this limit, we identify all surface terms of the algebra and give the explicit expression of the Hamiltonian in agreement with the previous formulation of it. The symmetry under area preserving diffeomorphisms, connected and nonconnected to the identity, is also discussed. Only parabolic $Sl(2,\mathbb{Z})$ discrete symmetries are preserved.