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.
Highlights
While in the general N = 2 case the protected chiral algebra has no residual supersymmetry, the chiral algebra associated to an N = 4 SCFT contains the small N = 4 superconformal algebra (SCA) as a subalgebra
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
N = 4 SYM theory is dual to IIB string theory on AdS5 × S5, with the 1/N expansion on the field theory side corresponding to the genus expansion on the string theory side
Summary
The super chiral algebra generator of dimension h transforms in the spin h representation of su(2)F. This is a BPS condition — the generators with h > 1 are the highest-weight states of short representations of the N = 4 subalgebra.. It is not known whether the chiral algebra for fixed N > 2 admits a deformation to general values of the central charge For this special value of c2d one finds several null relations that might be essential to ensure associativity of the operator algebra. We will address the simpler question of finding a holographic description for the leading large N limit of the chiral algebra, in terms of a classical field theory in the bulk. There are two ways we can imagine to proceed: attempting to construct the bulk theory by bottom-up guesswork; or deriving it from the top-down as a subsector of AdS5 × S5 string field theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
