Massive dressing factors for mixed-flux AdS$_3$/CFT$_2$

TL;DR

This paper refines the understanding of dressing factors in mixed-flux AdS3/CFT2, proving their key properties, solving crossing equations, and connecting to known limits, thus advancing integrability in string theory.

Contribution

It provides a detailed analysis and proof of the properties of dressing factors for mixed-flux AdS3 backgrounds, including unitarity, invariance, and solutions to crossing equations, extending previous work.

Findings

Dressing factors are unitary and CP-invariant in string kinematics.

They are parity invariant in mirror kinematics.

Results agree with known limits in pure RR flux and relativistic regimes.

Abstract

We follow up on our proposal for dressing factors for the mixed-flux $AdS_3\times S^3\times T^4$ background presented in arXiv:2402.11732. We discuss in detail the analytic properties of the dressing factors in the string and mirror kinematics for fundamental massive particles and bound states. We prove that the dressing factors are unitary and CP-invariant in the string kinematics, parity invariant in the mirror, and solve the crossing equations in both kinematics. In the limit of pure Ramond-Ramond flux they reduce to the known ones. Finally, we present their expansion at strong tension, as well as in the (small-RR-flux) relativistic limit, finding agreement with the literature.