Free field realization of superstring theory on AdS3

TL;DR

This paper extends Coulomb gas methods to SL(2,R) WZW models, enabling free field representations of superstring states on AdS3, including spectral flow and correlation functions, advancing the understanding of string dynamics in AdS3 backgrounds.

Contribution

It introduces a free field realization of superstring vertex operators on AdS3 incorporating spectral flow and computes key correlation functions and scattering amplitudes.

Findings

Derived two and three point functions for superstring states.

Included spectral flow symmetry in the free field framework.

Analyzed winding number violating scattering amplitudes.

Abstract

The Coulomb gas representation of expectation values in SU(2) conformal field theory developed by Dotsenko is extended to the SL(2,R) WZW model and applied to bosonic string theory on AdS3 and to Type II superstrings on AdS3 x N. The spectral flow symmetry is included in the free field realization of vertex operators creating superstring states of both Ramond and Neveu-Schwarz sectors. Conjugate representations for these operators are constructed and a background charge prescription is designed to compute correlation functions. Two and three point functions of bosonic and fermionic string states in arbitrary winding sectors are calculated. Scattering amplitudes that violate winding number conservation are also discussed.