Genus-2 holographic correlator on AdS5\xd7 S5 from localization

Abstract

We consider the four-point function of the stress tensor multiplet superprimary in mathcal{N} = 4 super-Yang-Mills (SYM) with gauge group SU(N ) in the large N and large ’t Hooft coupling lambda equiv {g}_{mathrm{YM}}^2N limit, which is holographically dual to the genus expansion of IIB string theory on AdS5× S5. In [1] it was shown that the integral of this correlator is related to derivatives of the mass deformed mathcal{N} = 2∗ sphere free energy, which was computed using supersymmetric localization to leading order in 1/N2 for finite λ. We generalize this computation to any order in 1/N2 for finite λ using topological recursion, and use this any order constraint to fix the R4 correction to the holographic correlator to any order in the genus expansion. We also use it to complete the derivation of the 1-loop supergravity correction, and show that analyticity in spin fails at zero spin in the large N expansion as predicted from the Lorentzian inversion formula. In the flat space limit, the R4 term in the holographic correlator matches that of the IIB S-matrix in 10d, which is a precise check of AdS5/CFT4 for local operators at genus-one. Using the flat space limit and localization we then fix D4R4 in the holographic correlator to any order in the genus expansion, which is nontrivial at genus-two, i.e. 1/N6. This is the first result at two orders beyond the planar limit at strong coupling for a holographic correlator.