Integration Measure and Spectral Flow in the Critical N=2 String

TL;DR

This paper explores the moduli space of a critical N=2 string, deriving the string measure for amplitudes, and introduces spectral-flow operators that connect different instanton sectors, with explicit computations of tree and loop amplitudes.

Contribution

It introduces a comprehensive analysis of the moduli space and measures for the critical N=2 string, including novel spectral-flow operators linking instanton sectors.

Findings

Derived the string measure for n-point amplitudes at arbitrary genus.

Introduced spectral-flow operators connecting instanton sectors.

Computed explicit tree and loop amplitudes.

Abstract

I present the moduli space of the (2+2)-dimensional critical closed fermionic string with two world-sheet supersymmetries. The integration of fermionic and Maxwell moduli in the presence of punctures yields the string measure for n-point amplitudes at arbitrary genus and instanton number. Generalized picture-changing and spectral-flow operators emerge, connecting different instanton sectors. Tree and loop amplitudes are computed.