Stringy horizons and generalized FZZ duality in perturbation theory

TL;DR

This paper derives and verifies dualities between different two-dimensional string theory models on black hole backgrounds using perturbation theory, confirming the generalized FZZ duality for specific scattering amplitudes.

Contribution

It provides a perturbative derivation of the FZZ duality and proves the generalized FZZ duality for tree-level maximally winding violating n-point amplitudes.

Findings

Derived FZZ duality using perturbation theory and Selberg integral relations.

Confirmed that certain sine-Liouville correlation functions match gauged WZW model correlators.

Proved GFZZ duality for tree-level maximally winding violating n-point amplitudes.

Abstract

We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n-2 winding modes actually coincide with the correlation functions in the SL(2,R)/U(1) gauged WZW model that include n-2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference arXiv:1603.05822. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary $n$. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.