Exact chiral ring of AdS(3)/CFT(2)

TL;DR

The paper presents an exact worldsheet calculation of tree-level three-point functions for chiral operators in string theory on $AdS_3\times S^3\times T^4$ with NS-NS flux, using the $SL(2,\mathbb{R})_k$ and $SU(2)_k$ WZW models. A crucial cancelation between the $H_3^+$ and $SU(2)$ structure constants yields a simple, factorized form that, after fixing the remaining free parameter $\nu$ in the $H_3^+$ sector, matches precisely with the fusion rules and structure constants of the $N=2$ chiral ring of the boundary symmetric product orbifold $\mathrm{Sym}^N(T^4)$ at large $N$. The bulk spectrum of chiral operators is organized into three holomorphic families $\mathcal{O}_h(x,y)$ built from $\Phi_h(x)$ and $V_{h-1}(y)$, together with Ramond-sector descendants, reproducing the boundary spectrum and correlators, including the nontrivial three-point functions. The results provide strong evidence for a non-renormalization-type principle in this AdS$_3$/CFT$_2$ setting and open avenues for higher-loop tests and potential integrable structures. Key fixed quantity is $\nu = \frac{2\pi}{b^4 \gamma(1+b^2)}$, with $b=1/\sqrt{k}$, ensuring exact boundary–bulk agreement of the chiral ring data.

Abstract

We carry out an exact worldsheet computation of tree level three-point correlators of chiral operators in string theory on AdS(3) x S^3 x 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 H3+ 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 H3+ 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.