Abstract
\( \mathcal{N}=4 \) 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 \( \mathcal{N}=4 \) 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 \( {\mathfrak{g}}_F=\mathfrak{s}\mathfrak{u}{(2)}_F \). Localization yields Chern-Simons theory on AdS3 with gauge algebra \( {\mathfrak{g}}_F \), whose boundary dual is the affine Lie algebra \( {\widehat{\mathfrak{g}}}_F \). 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.
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Bonetti, F., Rastelli, L. Supersymmetric localization in AdS5 and the protected chiral algebra. J. High Energ. Phys. 2018, 98 (2018). https://doi.org/10.1007/JHEP08(2018)098
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DOI: https://doi.org/10.1007/JHEP08(2018)098