Genus-2 holographic correlator on AdS5 × S5 from localization

We consider the four-point function of the stress tensor multiplet superprimary in $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) with gauge group SU(N ) in the large N and large ’t Hooft coupling $$ \lambda \equiv {g}_{\mathrm{YM}}^2N $$ 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 $$ \mathcal{N} $$ 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.