Exploring the Quantum Spectral Curve for AdS3/CFT2
Andrea Cavaglià, Simon Ekhammar, Nikolay Gromov, Paul Ryan
Abstract
A bstract Despite the rich and fruitful history of the integrability approach to string theory on the AdS 3 × S 3 × 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. In other integrable superstring backgrounds there is compelling evidence that this formulation captures all wrapping effects exactly and describes the full planar spectrum. This great success motivates us to study the new proposed QSC and develop methods to extract from it concrete predictions for spectral data. The AdS 3 × S 3 × T 4 case presents a significant novel feature and challenge compared to its higher-dimensional analogues — massless modes. It has been conjectured that these 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 4 SYM. In this paper we resolve these difficulties and obtain the first ever predictions for unprotected string excitations in the planar limit with finite quantum numbers and RR flux. We explain how to extract a systematic expansion around the analogue of the weak ’t Hooft coupling limit in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> = 4 SYM and also obtain high-precision numerical results. These concrete data and others obtainable from the QSC could help to identify the so-far mysterious dual CFT.