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 AdS₅ × S⁵. 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 AdS₅, for which a convenient off-shell description is available. This model can be viewed as the simplest truncation of the full AdS₅ × S⁵ 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 AdS₃ with gauge algebra g_F, whose boundary dual is the affine Lie algebra g^ _F. 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.