Avoiding the theorem of Lerche and Shore

TL;DR

This paper discusses the issues with defining supersymmetric sigma-models via constrained linear theories, presents a counterexample involving membranes in superstring theories, and highlights the role of central charges in supercharge algebra.

Contribution

It provides a counterexample demonstrating that well-defined Kahler subsectors do not directly originate from constrained linear supersymmetric theories.

Findings

Supersymmetric sigma-models constrained from linear theories are ill-defined.

A counterexample involving membranes in superstring theories is presented.

Central charges modify the supercharge algebra significantly.

Abstract

Supersymmetric $\sigma$-models obtained by constraining linear supersymmetric field theories are ill defined. Well defined subsectors parametrising Kahler manifolds exist but are not believed to arise directly from constrained linear ones. A counterexample is offered using improved understanding of membranes in superstring theories leading to crucial central terms modifying the algebra of supercharge densities