Supersymmetric Localization in AdS${}_5$ and the Protected Chiral Algebra

Abstract

$\mathcal{N}=4$ super Yang-Mills theory admits \cite{Beem:2013sza} 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 $Ad{S}_5\times S^5$. 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 $\mathcal{N}=4$ vector multiplet in $Ad{S}_5$, for which a convenient off-shell description is available. This model can be viewed as the simplest truncation of the full $Ad{S}_5\times S^5$ supergravity, in which case the vector multiplet should be taken in the adjoint representation of ${\mathfrak{g}}_F=\mathfrak{su}(2{)}_F$. Localization yields Chern-Simons theory on $Ad{S}_3$ with gauge algebra ${\mathfrak{g}}_F$, whose boundary dual is the affine Lie algebra ${\hat{\mathfrak{g}}}_F$. We comment on the generalization to the full bulk theory. We propose that the large $N$ limit of the chiral algebra of $\mathcal{N}=4$ SYM is again dual to Chern-Simons theory, with gauge algebra a suitable higher-spin superalgebra.

arXiv comment36 pages

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Cited by in corpus (1)

• Macdonald Index and Chiral Algebra