Quantum Spectral Curve for AdS3/CFT2: a proposal

Abstract

We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 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 AdS5 and AdS4 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.

Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2

“…In this paper we have derived for the first time the mirror thermodynamic Bethe ansatz equations for AdS 3 × S 3 × T 4 . Unlike previous attempts to the same end [49][50][51][52], our treatment does not rely on any truncation or limit. While some of the features of AdS3/CFT2 integrability have been long known [44][45][46], a key ingredient of our derivation has been the proposal of a new set of dressing factors [39] with nice self-consistent properties in the mirror-mirror kinematics and under fusion -something that was not obvious in previous proposals [47,48].…”

“…On the other hand, it would also be interesting to further simplify these equations and recast them in terms of a T-system, and eventually in terms of a quantum spectral curve. The final result of this simplification procedure may be related to the quantum spectral curve bootstrapped in [51,52], in which case it should clarify how the massless modes feature in that formalism. The advantage in this reformulation is that the quantum spectral curve should be a more efficient computational framework, and it may also help unveil some of the underlying symmetry structures of the theory.…”

“…The aim of this article is to derive the mirror TBA equations for the pure-RR AdS 3 × S 3 ×T 4 background. Some attempts in this directions were already made in [49][50][51][52]. In [49], a set of TBA equations was derived for a system obtained by first truncating the spectrum to the massless modes and then taking a relativistic limit.…”

“…As such, neglecting some types of particles may lead to drastically different results -in other words, there are no closed subsectors in the finite-volume theory. More recently, the authors of [51,52] have independently proposed the quantum spectral curve for a model with psu(1, 1|2) ⊕ psu(1, 1|2) symmetry. Their approach bypassed the derivation of the mirror TBA altogether, and instead relied on a symmetry bootstrap.…”

“…It seems that the resulting equations capture some features of the AdS 3 ×S 3 ×T 4 Bethe-Yang equations; however, it is not clear if they account for the massless modes and how. 1 Ultimately, the validity of the proposals [51,52] will boil down to whether the quantum-spectral curve construction is uniquely constrained by symmetries, even for models whose symmetries are not given by a simple Lie (super)algebra, which is an outstanding question.…”