D=5 Simple Supergravity on AdS_{3} x S^{2} and N=4 Superconformal Field Theory

TL;DR

The paper analyzes the Kaluza-Klein spectrum of $D=5$ simple supergravity on $AdS_3\times S^2$ and its holographic relation to a two-dimensional $N=4$ SCFT. By expanding fields on $S^2$ and applying Freund-Rubin-like backgrounds, it uncovers an unusual self-duality for massive vectors and organizes all KK modes into short $SU(1,1|2)$ representations, paired with left-moving $SL(2,\mathbb{R})_L$ structure, via an oscillator construction. Conformal weights of boundary operators are computed from asymptotic wavebehaviors, showing that all towers fall into four infinite chiral-primary multiplets, a result compatible with AdS/CFT and reminiscent of known higher-dimensional supergravity compactifications. The work also discusses the possible extension to $OSp(2,2|2;-1)$ and the implications for a 2D CFT with a semi-direct product symmetry, highlighting a deep parallel between $D=5$ simple supergravity and M-theory compactifications.

Abstract

We study the Kaluza-Klein spectrum of D=5 simple supergravity on $S^2$ with special interest in the relation to a two-dimensional N=4 superconformal field theory. The spectrum is obtained around the maximally supersymmetric Freund-Rubin-like background $AdS_3\times S^2$ by closely following the well-known techniques developed in D=11 supergravity. All the vector excitations turn out to be ``(anti-)self-dual'', having only one dynamical degree of freedom. The representation theory for the Lie superalgebra $SU(1,1|2)$ is developed by means of the oscillator method. We calculate the conformal weight of the boundary operator by estimating the asymptotic behavior of the wave function for each Kaluza-Klein mode. All the towers of particles are shown to fall into four infinite series of chiral primary representations of $SU(1,1|2)\times SL(2,{\bf R})$ (direct product), or $OSp(2,2|2;-1)\cong SU(1,1|2)\times SL(2,{\bf R})$ (semi-direct product).

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