D=5 Simple Supergravity on AdS_{3} x S^{2} 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 $Ad{S}_3\times S^2$ 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 $SU(1,1|2)\times SL(2,\mathbf{R})$ (direct product), or $OSp(2,2|2;-1)\cong SU(1,1|2)\times SL(2,\mathbf{R})$ (semi-direct product).

34 pages, 7 figures, revised version

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