An alternative BRST operator for topological Landau-Ginzburg models

TL;DR

This paper introduces a new BRST operator for topological Landau-Ginzburg models that resolves ghost number issues and clarifies the gauge fixing process, emphasizing the role of anti-BRST symmetry in topological field theories.

Contribution

It proposes a novel BRST operator for N=2 Landau-Ginzburg models that addresses fractional ghost numbers and incorporates anti-BRST symmetry to establish topological nature.

Findings

New BRST operator resolves ghost number issues

Anti-BRST operator is identified as an N=2 supersymmetry

Physical observable space remains unchanged

Abstract

We propose a new BRST operator for the B-twist of $N=2$ Landau-Ginzburg (LG) models. It solves the problem of the fractional ghost numbers of Vafa's old BRST operator and shows how the model is obtained by gauge fixing a zero action. An essential role is played by the anti-BRST operator,which is given by one of the supersymmetries of the $N=2$ algebra. Its presence is needed in proving that the model is indeed a topological field theory. The space of physical observables, defined by taking the anti-BRST cohomology in the BRST cohomology groups, is unchanged.