AdS/CFT dualities involving large 2d N=4 superconformal symmetry

TL;DR

The paper analyzes AdS3/CFT2 dualities where the boundary theory has large N=4 superconformal symmetry ${\cal A}_{\gamma}$. It derives the bulk Kaluza-Klein spectrum on $AdS_3 \times S^3 \times S^3 \times S^1$ from representation theory and proposes a boundary SCFT realized as a sigma-model on ${\rm Sym}^{k^-}(U(2))$ with flux and discrete gauge data, connected to symmetric-product orbifolds in special limits. By examining both M-theory and IIB brane setups, the authors relate bulk spectra to boundary operators and explore the role of the nonlinear tilde algebra ${\tilde{\cal A}}_{\gamma}$ in organizing chiral states. They further develop sigma-model realizations for ${\cal A}_{\gamma}$ symmetry, identifying regimes where a weakly coupled description exists, and discuss D-brane perturbations and open problems for a precise nonperturbative formulation. Overall, the work provides a framework for understanding AdS3/CFT2 dualities with maximal 2d $N=4$ symmetry, highlighting the intricate interplay between bulk KK spectra, boundary chiral structure, and sigma-model realizations.

Abstract

We study the duality between string theory on AdS_3 X S^3 X S^3 and two-dimensional conformal theories with large N=4 superconformal algebra A_gamma. We discuss configurations of intersecting branes which give rise to such near-horizon geometries. We compute the Kaluza-Klein spectrum and propose that the boundary superconformal theory can be described by a sigma model on a suitable symmetric product space with a particular choice of anti-symmetric two-form.