Integrable bootstrap for AdS3/CFT2 correlation functions

Abstract

We propose an integrable bootstrap framework for the computation of correlation functions for superstrings in AdS3 × S3 × T4 backgrounds supported by an arbitrary mixture or Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. The framework extends the “hexagon tessellation” approach which was originally proposed for AdS5 × S5 and for the first time it demonstrates its applicability to other (less supersymmetric) setups. We work out the hexagon form factor for two-particle states, including its dressing factors which follow from those of the spectral problem, and we show that it satisfies non-trivial consistency conditions. We propose a bootstrap principle, slightly different from that of AdS5 × S5, which allows to extend the form factor to arbitrarily many particles. Finally, we compare its predictions with some correlation functions of protected operators. Possible applications of this construction include the study of wrapping corrections, of higher-point correlation functions, and of non-planar corrections.

Massless S matrices for AdS3/CFT2

“…They proposed a rapidity variable γ(p) for massless particles, similar to the one discussed in AdS5/CFT4 by Beisert, Hernandez and Lopez [27], 1 The case of pure-NSNS backgrounds can also be thoroughly understood by integrability [9,10] (including when the WZW level has the special value k = 1 [6,11]), while the mixed-flux theories show signs of being integrable but appear to have a much more complicated dynamics [12][13][14][15]. 2 The computation of three- [16] and higher-point [17,18] correlation functions by integrability saw significant advances recently, including in AdS3/CFT2 [19], but it is far from being completely understood.…”

“…We should stress that this discussion of the S matrices is perfectly compatible with that of refs. [24,25], see also [19] for a concise summary of the results. In those references, the expressions for the S matrix involve only the Zhukovsky parameters x ± p and x p which are valid for any value of p. The trouble only comes when we try to express the S matrix in terms of p itself, or of the rapidity γ p , because as we have seen the relation between x p and p, and between γ p and p, is not analytic.…”

“…The complete discussion of the representations and the resulting S matrix is somewhat scattered throughout the literature, unfortunately with varying notations. A recent rather complete summary of the main results can be found in[19].…”

New Dressing Factors for AdS3/CFT2

“…This is particularly exciting in view of the obvious physical significance of the setup: it interpolates between the pure-RR case which we studied here (and which is reminiscent of AdS 5 × S 5 ) and the pure-NSNS case which can be described as a Wess-Zumino-Witten model [19] and studied in great detail, both by integrability [20,21] and by worldsheet CFT techniques [22][23][24]. Finally, it would be interesting to see how this proposal for the dressing factors would amend the current understanding of the hexagon formalism [56][57][58] for AdS 3 × S 3 × T 4 , whose study has been recently initiated [33].…”

“…It is possible to derive the matrix part of the S matrix [31] and express it in terms of the Zhukovsky variables (following the notation of [33])…”