On the field-antifield (a)symmetry of the pure spinor superstring

TL;DR

This paper extends the pure spinor superstring cohomology analysis to antifields, revealing new algebraic structures and properties of the ghost number two cohomology, with implications for understanding the b ghost and physical states.

Contribution

It introduces an extended DDF algebra approach to analyze pure spinor cohomology at higher ghost numbers, especially antifields, and explores the properties of the b ghost in this context.

Findings

Extended DDF algebra describes ghost number two cohomology.

DDF conjugates of the b ghost zero mode are identified.

Physical state conditions are discussed within the extended framework.

Abstract

In this work, the DDF-like approach to the pure spinor cohomology is extended to the next ghost number level, the so called antifields. In a direct (supersymmetric) parallel to the bosonic string, some properties of the ghost number two cohomology are derived with the enlargement of the DDF algebra. Also, the DDF conjugates of the b ghost zero mode emerge naturally from the extended algebra and the physical state condition is discussed. Unlike the bosonic string case, the cohomology analysis of the pure spinor b ghost is restricted to BRST-closed states.