We employ the free field realisation of the $$ \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 $$ psu 1 1 2 1 world-sheet theory to constrain the correlators of string theory on AdS3× S3× 𝕋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 by the (genus zero) world-sheet — this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable ‘incidence relation’ obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.

Building on arXiv:1804.01998 we investigate the integrable structure of the Wess-Zumino-Witten (WZW) model describing closed strings on AdS 3 × S 3 × T 4 . Using the recently-proposed integrable S matrix we show analytically that all wrapping corrections cancel and that the theory has a natural spin-chain interpretation. We construct the integrable spin chain and discuss its relation with the WZW description. Finally we compute the spin-chain spectrum in closed form and show that it matches the WZW prediction on the nose. arXiv:1806.00422v2 [hep-th] The correspondence between gravity on AdS 3 and conformal field theory in two dimensions (CFT 2 ) is a key example of holographic duality [1,2]. From the seminal work of Brown and Henneaux [3] to the remarkable developments in string theory [4], see e.g. ref.[5] for a review, the AdS 3 /CFT 2 correspondence stands out for the possibility of performing exact computations by conformal field theory techniques. In string theory such techniques arise in two distinct ways. Firstly, the dual conformal field theory is two-dimensional and, at weak string tension, is described by an almost-free CFT-more specifically, by the symmetric-product orbifold of a free CFT. Secondly, there exist superstring backgrounds that are supported by Neveu-Schwarz-Neveu-Schwarz (NS-NS) fluxes only. These can be described by a CFT 2 on the worldsheet, without the usual complications due to Ramond-Ramond (R-R) fluxes [6]. Such a CFT 2 involves an sl(2, R) Wess-Zumino-Witten model describing (the chiral part of) AdS 3 , which can be studied in detail following Maldacena and Ooguri [7], see also refs. [8][9][10][11][12].A more recent development is that strings on maximally supersymmetric AdS 3 backgrounds are classically integrable [13][14][15], and indeed this integrability seems to carry over to the quantum theory when this is constructed in light-cone gauge, see ref.[16] for a review (see also refs. [17, 18] for broader reviews of AdS/CFT integrability). More specifically, an exact worldsheet scattering matrix was constructed for strings on R-R backgrounds [19][20][21] and the relevant dressing factors were proposed [22][23][24]. Quite remarkably, even backgrounds supported by a mixture of R-R and NS-NS fluxes are classically integrable [15] and their S matrix can similarly be determined [25][26][27], though no proposal exists for the dressing factors yet. Curiously, until recently no proposal for the worldsheet S matrix at the pure NS-NS point existed-despite the fact that, at least in the RNS formalism, the resulting theory is substantially simpler than a generic mixed-flux one. Technically this is due to the fact that the light-cone symmetry algebra contracts at the NS-NS point. 1 Recently, in ref.[31], an exact integrable worldsheet S matrix for strings on AdS 3 × S 3 × T 4 with pure-NS-NS fluxes was proposed by a different approach, based on TT deformations [32][33][34][35]. This S matrix, including its dressing factor, is much simpler than its mixed-flux [27] (or even pure-R-R [36]) count...

We revisit the computation of string worldsheet correlators on Euclidean AdS3 with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.

We exploit null vectors of the fractional Virasoro algebra of the symmetric product orbifold to compute correlation functions of twist fields in the large N limit. This yields a new method to derive correlation functions in these orbifold CFTs that is purely based on the symmetry algebra. We explore various generalisations, such as subleading (torus) contributions or correlation functions of other fields than the bare twist fields. We comment on the consequences of our computation for the AdS 3 /CFT 2 correspondence.

We compute the tree-level bosonic S matrix in light-cone gauge for superstrings on pure-NSNS AdS 3 ×S 3 ×S 3 ×S 1. We show that it is proportional to the identity and that it takes the same form as for AdS 3 × S 3 × T 4 and for flat space. Based on this, we make a conjecture for the exact worldsheet S matrix and derive the mirror thermodynamic Bethe ansatz (TBA) equations describing the spectrum. Despite a non-trivial vacuum energy, they can be solved in closed form and coincide with a simple set of Bethe ansatz equations-again much like AdS 3 × S 3 × T 4 and flat space. This suggests that the model may have an integrable spin-chain interpretation. Finally, as a check of our proposal, we compute the spectrum from the worldsheet CFT in the case of highest-weight representations of the underlying Kač-Moody algebras, and show that the mirror-TBA prediction matches it on the nose.