Genus-2 holographic correlator on AdS5 × S5 from localization

We consider the four-point function of the stress tensor multiplet superprimary in N N = 4 super-Yang-Mills (SYM) with gauge group SU(N ) in the large N and large ’t Hooft coupling λ ≡ gYM²N λ ≡ g YM 2 N limit, which is holographically dual to the genus expansion of IIB string theory on AdS5 × S 5. In [1] it was shown that the integral of this correlator is related to derivatives of the mass deformed N N = 2 ∗ sphere free energy, which was computed using supersymmetric localization to leading order in 1/N 2 for finite λ. We generalize this computation to any order in 1/N 2 for finite λ using topological recursion, and use this any order constraint to fix the R 4 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 R 4 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 D 4 R 4 in the holographic correlator to any order in the genus expansion, which is nontrivial at genus-two, i.e. 1/N 6. This is the first result at two orders beyond the planar limit at strong coupling for a holographic correlator.