Homotopy Operators and Identity-Based Solutions in Cubic Superstring Field Theory

TL;DR

This paper constructs nilpotent operators using BRST currents in superstring theory, explores their realization as kinetic operators in cubic superstring field theory, and analyzes their cohomological properties.

Contribution

It introduces a new class of nilpotent operators and demonstrates their role as kinetic operators in identity-based solutions within cubic superstring field theory.

Findings

Construction of nilpotent operators from BRST currents.

Realization of these operators as kinetic operators in the theory.

Analysis of homotopy operators and cohomology relationships.

Abstract

We construct a class of nilpotent operators using the BRST current and ghost fields in superstring theory. The operator can be realized in cubic superstring field theory as a kinetic operator in the background of an identity-based solution. For a particular type of the deformed BRST operators, we find a homotopy operator and discuss its relationship to the cohomology in a similar way to the bosonic case, which has been elaborated by the authors.