Exploring the Quantum Spectral Curve for AdS${}_3$/CFT${}_2$

TL;DR

This paper advances the understanding of the Quantum Spectral Curve for AdS3/CFT2, overcoming technical challenges to produce the first predictions for string excitations and offering data to identify the dual CFT.

Contribution

It resolves technical difficulties in solving the QSC with non-quadratic branch cuts and provides the first predictions for generic unprotected string states in AdS3/CFT2.

Findings

First predictions for generic unprotected string excitations.

Systematic expansion around weak coupling limit.

High-precision numerical results for the QSC.

Abstract

Despite the rich and fruitful history of the integrability approach to string theory on the $AdS_3\times S^3\times T^4$ background, it has not been possible to extract many concrete predictions from integrability, except in a strict asymptotic regime of large quantum numbers, due to the severity of wrapping effects. The situation changed radically with two independent and identical proposals for the Quantum Spectral Curve (QSC) for this system in a background of pure Ramond-Ramond flux. This formulation is expected to capture all wrapping effects exactly and describe the full planar spectrum. Massless modes conjecturally manifest themselves in a new property of this QSC: the non-quadratic nature of the branch-cut singularities of the QSC Q-functions. This feature implies new technical challenges in solving the QSC equations as compared to the well-studied case of N=4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for generic unprotected string excitations. We explain how to extract a systematic expansion around the analogue of the weak 't Hooft coupling limit in N=4 SYM and also obtain high-precision numerical results. This concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.