Non-Relativistic Four Dimensional p-Brane Supersymmetric Theories and Lie Algebra Expansion

TL;DR

This paper uses Lie algebra expansion to derive non-relativistic supersymmetric theories for strings and membranes from four-dimensional supergravity, expanding the algebraic framework for p-brane models.

Contribution

It introduces a novel application of Lie algebra expansion to generate non-relativistic supersymmetric p-brane theories from 4D supergravity.

Findings

Derived two non-relativistic supersymmetric theories for strings and membranes.

Established a method to decompose super-Poincaré algebra for p-brane models.

Demonstrated the feasibility of obtaining non-relativistic limits via algebra expansion.

Abstract

We apply the Lie algebra expansion method to the $\mathcal{N}=1$ super-Poincar\'e algerba in four dimensions. We define a set of p-brane projectors that induce a decomposition of the super-Poincar\'e algebra preparatory for the expansion. We show that starting from the $\mathcal{N}=1$ supergravity action in four dimensions it is possible to obtain two non-relativistic supersymmetric theories, one describing strings, the other membranes.