Path-Integral Quantization of the (2,2) String

TL;DR

This paper provides a comprehensive analysis of the (2,2) NSR string in flat (2+2) dimensions, covering path integrals, gauge fixing, supermoduli space, and instanton configurations, advancing the understanding of its quantum structure.

Contribution

It offers a detailed treatment of superconformal gauge fixing, supermoduli space analysis, and chiral bosonization for the (2,2) string, including new insights into picture-changing and left-right mover combinations.

Findings

Explicit construction of background gauge fields in all instanton sectors

Development of chiral bosonization on higher-genus punctured surfaces

Identification of two different three-point functions from left-right mover combinations

Abstract

A complete treatment of the (2,2) NSR string in flat (2+2) dimensional space-time is given, from the formal path integral over N=2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We perform in detail the superconformal gauge fixing, discuss the spectral flow, and analyze the supermoduli space with emphasis on the gauge moduli. Background gauge field configurations in all instanton sectors are constructed. We develop chiral bosonization on punctured higher-genus surfaces in the presence of gauge moduli and instantons. The BRST cohomology is recapitulated, with a new space-time interpretation for picture-changing. We point out two ways of combining left- and right-movers, which lead to different three-point functions.