Correlators in AdS_3 string theory

TL;DR

This paper reviews the computation of correlation functions in AdS_3 string theory using Coulomb gas methods, introduces a formalism incorporating spectral flow and winding numbers, and presents new results for winding number violating processes.

Contribution

It extends the Coulomb gas approach to AdS_3 string theory, including spectral flow and winding numbers, and derives new expressions for non-conserving winding number amplitudes.

Findings

Two and three point tachyon amplitudes computed match previous results.

New formulas for processes violating winding number conservation.

Formalism naturally incorporates spectral flow symmetry.

Abstract

The computation of two and three point functions in the Coulomb gas free field approach to string theory in the SL(2,R)/U(1) black hole background is reviewed. An interesting relation arises when comparing the results obtained using two different screening operators. The formalism is then modified to study string theory propagating in AdS$_3$ which is considered as the direct product of the SL(2)/U(1) coset times a timelike free boson. This representation allows to naturally include the spectral flow symmetry and winding number in vertex operators and correlation functions. Two and three point tachyon amplitudes are computed in this new scenario and the results coincide with previous reports in the literature. Novel expressions are found for processes violating winding number conservation.