D=5 simple supergravity on AdS3× S2 and N=4 superconformal field theory

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× 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)× SL(2, R) (direct product), or OSp(2,2|2;−1)≅ SU(1,1|2)× SL(2, R) (semi-direct product).