Supersymmetric localization in AdS5 and the protected chiral algebra

N = 4 super Yang-Mills theory admits [1] a protected subsector isomorphic to a two-dimensional chiral algebra, obtained by passing to the cohomology of a certain supercharge. In the large N limit, we expect this chiral algebra to have a dual description as a subsector of IIB supergravity on AdS(5) x S-5. This subsector can be carved out by a version of supersymmetric localization, using the bulk analog of the boundary supercharge. We illustrate this procedure in a simple model, the theory of an N = 4 vector multiplet in AdS(5), for which a convenient off-shell description is available. This model can be viewed as the simplest truncation of the full AdS(5) x S-5 supergravity, in which case the vector multiplet should be taken in the adjoint representation of g(F) = su(2)(F). Localization yields Chern-Simons theory on AdS(3) with gauge algebra gF, whose boundary dual is the affine Lie algebra (g) over capF. We comment on the generalization to the full bulk theory. We propose that the large N limit of the chiral algebra of N = 4 SYM is again dual to Chern-Simons theory, with gauge algebra a suitable higher-spin superalgebra.