BRST gauge fixing and the algebra of global supersymmetry

TL;DR

This paper investigates how gauge fixing affects the supersymmetry algebra in supersymmetric gauge theories, proposing a method to extract physical supersymmetry information despite gauge fixing breaking the symmetry.

Contribution

It introduces a prescription within the path integral framework to analyze and recover physical supersymmetry algebra in gauge-fixed supersymmetric theories, including complex cases like D-particles.

Findings

Supersymmetry charge density can be decomposed into naive and BRST exact parts.

Equal-time anti-commutator of SUSY charge includes a physical and a BRST exact component.

Method applied successfully to N=1, N=2 SYM theories and D=10 superparticle cases.

Abstract

A global supersymmetry (SUSY) in supersymmetric gauge theory is generally broken by gauge fixing. A prescription to extract physical information from such SUSY algebra broken by gauge fixing is analyzed in path integral framework. If $\delta_{SUSY}\delta_{BRST}\Psi = \delta_{BRST}\delta_{SUSY}\Psi$ for a gauge fixing ``fermion'' $\Psi$, the SUSY charge density is written as a sum of the piece which is naively expected without gauge fixing and a BRST exact piece. If $\delta_{SUSY}\delta_{SUSY}\delta_{BRST}\Psi = \delta_{BRST}\delta_{SUSY}\delta_{SUSY}\Psi$, the equal-time anti-commutator of SUSY charge is written as a sum of a physical piece and a BRST exact piece. We illustrate these properties for N=1 and N=2 supersymmetric Yang-Mills theories and for a D=10 massive superparticle (or ``D-particle'') where the $\kappa$-symmetry provides extra complications.