Gso Projection, BRST Cohomology and Picture-Changing in N=2 String Theory

TL;DR

This paper analyzes the BRST cohomology, GSO projections, and picture-changing mechanisms in critical N=2 fermionic string theory, revealing the structure of massless states, their interactions, and the implications for spacetime supersymmetry.

Contribution

It provides a detailed study of the BRST cohomology, GSO projections, and picture-changing in N=2 string theory, including the construction of vertex operators and analysis of spacetime supersymmetry.

Findings

Twisted sectors contain non-local massless fermions.

Two GSO projections yield different massless spectra.

Spacetime supersymmetry generators are null operators.

Abstract

We investigate in detail the critical $N{=}2$ fermionic string with and without a global ${\bf Z}_2$ twist. An analysis of BRST cohomology shows that twisted sectors contain massless `spacetime' fermions which are {\it non-local\/} with respect to the standard massless boson. However, two distinct GSO projections exist, one (untwisted) retaining merely the usual boson and its spectral-flow partner, the other (twisted) yielding two fermions and one boson, on the massless level. The corresponding chiral BRST-invariant vertex operators are constructed in certain pictures, and their fusion and picture-changing are investigated, including the construction of inverse picture-changing operators. The $N{=}2$ `spacetime supersymmetry' generators are {\it null\/} operators, since the twisted massless states fail to interact. The untwisted three- and four-point functions are recalculated at tree-level.