Exact N=4 correlators of AdS(3)/CFT(2)

TL;DR

The paper extends the AdS3/CFT2 correspondence to chiral $N=4$ operators, comparing exact bulk three-point functions in type IIB string theory on $AdS_3\times S^3\times M^4$ with boundary correlators of the symmetric orbifold CFT of $M^4$. It provides a closed-form bulk expression for these correlators, expressed in a factorized holomorphic/antiholomorphic form, and demonstrates exact agreement with boundary results of Lunin:2001pw for all $N=4$ chiral cases (including $M^4=T^4$) and extends to new bulk correlators for the $T^4$ case not previously computed on the boundary. The results rely on the $SL(2,R)_{k+2}$ and $SU(2)_{k-2}$ WZW structures and use $L(J_i,M_i)$ factors and $SU(2)$ 3j symbols to encode the fusion rules and selection rules. The discussion highlights the unexpected non-renormalization-like behavior across moduli space at large $N$ and outlines open questions regarding finite-$N$ corrections and the bulk interpretation of boundary fermion fusion choices.

Abstract

We extend to chiral N=4 operators the holographic agreement recently found between correlators of the symmetric orbifold of M^4 at large N and type IIB strings propagating in AdS(3) x S^3 x M^4, where M^4=T^4 or K3. We also present expressions for some bulk correlators not yet computed in the boundary.