Quantum Spectral Curve for AdS$_3$/CFT$_2$: a proposal

TL;DR

This paper proposes a Quantum Spectral Curve framework for string theory on AdS3/CFT2, demonstrating its consistency with known equations and highlighting novel features like non-quadratic branch cuts, advancing integrability methods in this context.

Contribution

It introduces a conjectured Quantum Spectral Curve for AdS3/CFT2, extending integrability techniques with new structural features and showing consistency with existing Bethe Ansatz results.

Findings

QSC reproduces asymptotic Bethe equations in the large-length regime

Identifies a novel non-quadratic branch cut structure in the QSC

Suggests the proposed QSC is complete and self-consistent

Abstract

We conjecture the Quantum Spectral Curve equations for string theory on $AdS_3 \times S^3 \times T^4$ with RR charge and its CFT$_2$ dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS$_5$ and AdS$_4$ cases, but contains a critical new feature - the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.