On the worldsheet S matrix of the AdS3/CFT2 mixed-flux mirror model

TL;DR

This paper investigates the integrability and reality conditions of the worldsheet S matrix in the AdS3/CFT2 mixed-flux mirror model, crucial for understanding the string spectrum in this complex background.

Contribution

It provides the first analysis of the tree-level S matrix for both original and mirror models in the mixed-flux AdS3 background, addressing integrability and spectrum reality issues.

Findings

Identified conditions for the integrability of the mirror model.

Analyzed the reality properties of the spectrum in the mixed-flux background.

Discussed the implications of a complex Hamiltonian on the mirror model's well-definedness.

Abstract

String on $AdS_3\times S^3\times T^4$ backgrounds are known to be classically integrable in the presence of a mixture of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. It is expected that this results in the existence of a well-defined factorised worldsheet S matrix. In order to use integrability to compute the string spectrum we need such a factorised S matrix to exist also for the "mirror" model, obtained by a double Wick rotation of the original worldsheet theory. In the mixed-flux case the mirror model has a complex Hamiltonian, which raises questions on its well-definedness. In the paper we study the worldsheet tree-level S matrix of the original and mirror model and discuss some necessary conditions for the integrability and reality of the spectrum.