Genus-2 holographic correlator on AdS5 × S5 from localization
Shai M. Chester
Abstract
A bstract We consider the four-point function of the stress tensor multiplet superprimary in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 super-Yang-Mills (SYM) with gauge group SU( N ) in the large N and large ’t Hooft coupling $$ \lambda \equiv {g}_{\mathrm{YM}}^2N $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> <mml:mo>≡</mml:mo> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>YM</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mi>N</mml:mi> </mml:math> limit, which is holographically dual to the genus expansion of IIB string theory on AdS 5 × S 5 . In [1] it was shown that the integral of this correlator is related to derivatives of the mass deformed $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 AdS 5 /CFT 4 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.