Central Extensions of Supersymmetry in Four and Three Dimensions

TL;DR

This paper explores the maximal central extensions of supertranslation algebras in three and four dimensions, linking tensor charges to topological defects and scalar moduli space configurations, with explicit examples from Calabi-Yau compactifications.

Contribution

It provides a detailed analysis of how tensor central charges relate to topological defects and moduli space configurations in extended supersymmetry theories.

Findings

Tensor central charges correspond to topological defects like membranes and strings.

Charges are related to nontrivial configurations on scalar moduli space.

Explicit realization of charges in N=2 theories from Calabi-Yau compactifications.

Abstract

We consider the maximal central extension of the supertranslation algebra in d=4 and 3, which includes tensor central charges associated to topological defects such as domain walls (membranes) and strings. We show that for all N-extended superalgebras these charges are related to nontrivial configurations on the scalar moduli space. For N=2 theories obtained from compactification on Calabi-Yau threefolds, we give an explicit realization of the moduli-dependent charges in terms of wrapped branes.