Chiral BRST Cohomology of N=2 Strings at Arbitrary Ghost and Picture Number

TL;DR

This paper computes the BRST cohomology of N=2 strings at various ghost and picture numbers, confirming the presence of a single massless state at non-zero momentum and revealing picture dependence at zero momentum.

Contribution

It provides a detailed computation of the BRST cohomology for N=2 strings at arbitrary ghost and picture numbers, including new insights into picture dependence at zero momentum.

Findings

Relative cohomology at non-zero momentum has a single massless state.

Absolute cohomology is derived using homological algebra methods.

Picture dependence is observed at zero momentum, similar to N=1 strings.

Abstract

We compute the BRST cohomology of the holomorphic part of the N=2 string at arbitrary ghost and picture number. We confirm the expectation that the relative cohomology at non-zero momentum consists of a single massless state in each picture. The absolute cohomology is obtained by an independent method based on homological algebra. For vanishing momentum, the relative and absolute cohomologies both display a picture dependence -- a phenomenon discovered recently also in the relative Ramond sector of N=1 strings by Berkovits and Zwiebach.