Exact chiral ring of AdS₃/CFT₂

Abstract

We carry out an exact worldsheet computation of tree level threepoint correlators of chiral operators in type IIB string theory on AdS 3 × S 3 × T 4 with NS-NS flux. We present a simple representation for the string chiral operators in the coordinate basis of the dual boundary CFT. Striking cancelations occur between the three-point functions of the H + 3 and the SU(2) WZW models which result in a simple factorized form for the final correlators. We show, by fixing a single free parameter in the H + 3 WZW model, that the fusion rules and the structure constants of the N = 2 chiral ring in the bulk are in precise agreement with earlier computations in the boundary CFT of the symmetric product of T 4 at the orbifold point in the large N limit.e-print archive: http://lanl.arXiv.org/abs/hep-th/0703022 ATISH DABHOLKAR AND ARI PAKMAN

Coulomb integrals for theSL(2,R)Wess-Zumino-Novikov-Witten model

“…Finally, the extension of our results both to higher-point functions and to the supersymmetric case, started in [32], might be relevant to the scope of verifying the AdS 3 /CFT 2 correspondence, another relevant issue which has not been completed yet (see [33,34,35] for some recent work in this direction). 6 Appendix: useful formulas…”

“…For future reference, it is convenient to recall here that these operators appear when looking for the asymptotic expressions of the following normalizable operators in the SL(2, 33) where x,x keep track of the SL(2, C) quantum numbers. These operators, when transformed to the m-basis through the following Fourier integral: 34) give, in the limit φ → ∞,…”

On the semiclassical three-point function inAdS3

“…In the full superstring theory the interrelation of the AdS 3 and S 3 contributions to the quantum 3-point correlator of BPS type fields has been described in [16], [17].…”

“…This motivated us to reconsider the problem and compute directly the semiclassical constant, generalising the method in [13], which was proposed originally as a semiclassical check of the quantum Liouville 3-point constant. While the quantum AdS 3 theory and its applications to the superstring on AdS 3 ×S 3 ×M 4 in the NS-NS background ( [16], [17] and references therein) is well studied, and, thus, this is no more than a toy model in the semiclassical context under consideration, the elaboration of 2d CFT techniques is important for the analogous unsolved problems in more realistic and less known cases.…”

Comments on the SN orbifold CFT in the large N-limit

“…A non-exhaustive list of examples includes instanton calculations [3], black hole physics [4], matrix string theory [5][6][7][8], and AdS/CFT correspondence [9][10][11][12][13][14][15][16][17][18][19][20][21]. Undoubtedly, on of the most exciting application of the orbifolds is in the context of the gauge/gravity duality [9,[22][23][24], with lots of recent activity [25][26][27][28][29][30][31].…”