Gluing Quantum Spectral Curves: A Two-Copy osp(4|2) Construction

TL;DR

This paper introduces a Quantum Spectral Curve for AdS3*S3*S3*S1 string theory, based on symmetry and integrability, successfully reproducing known equations and extending Bethe Ansatz to massless modes, with some unresolved puzzles.

Contribution

It proposes a new Quantum Spectral Curve for AdS3*S3*S3*S1, extending integrability tools and including massless modes, advancing non-perturbative analysis of this holographic system.

Findings

Reproduces crossing equations and Bethe equations in the large volume limit.

Extends Asymptotic Bethe Ansatz to include massless modes.

Identifies puzzles regarding crossing equations and unitarity for dressing phases.

Abstract

We propose a Quantum Spectral Curve for planar string theory on AdS3*S3*S3*S1 supported by pure Ramond-Ramond flux. Our proposal is built on symmetry considerations and integrability-based functional relations. To test our construction, we consider the large volume limit and successfully reproduce the cross- ing equations and the correct structure of the Bethe equations found in the literature. In a symmetric subsector, we find agreement with previously known results and furthermore extend the Asymptotic Bethe Ansatz to include massless modes. Beyond this sector, we identify an interesting puzzle regarding the compatibility of crossing equations with braiding unitarity for individual dressing phases, which warrants further investigation and may require additional physical insights or novel structures not previously encountered in related systems. As we expect the QSC to be exact in the planar limit, our proposal may open the way for non-perturbative analysis of this holographic system.