BRST gauge fixing and the algebra of global supersymmetry

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 $δ_{SUSY}δ_{BRST}Ψ= δ_{BRST}δ_{SUSY}Ψ$ for a gauge fixing ``fermion'' $Ψ$, 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 $δ_{SUSY}δ_{SUSY}δ_{BRST}Ψ= δ_{BRST}δ_{SUSY}δ_{SUSY}Ψ$, 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 $κ$-symmetry provides extra complications.