Summing up all genus free energy of ABJM matrix model.

The localization technique allows us to compute the free energy of the U( N) × U( N) Chern-Simons-matter theory dual to type IIA strings on AdS × CP from weak to strong 't Hooft coupling λ = N/ k at finite N, as demonstrated by Drukker, Mariño, and Putrov. In this note we study further the free energy at large 't Hooft coupling with the aim of testing AdS/CFT at the quantum gravity level and, in particular, sum up allthe1/ N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form - the Airy function, $ {\text{Ai}}\left( {{{\left( {{{{\pi {k^2}}} \left/ {{\sqrt {2} }} \right.}} \right)}^{{{2} \left/ {3} \right.}}}{\lambda_{\text{ren}}}} \right) $, with the renormalized 't Hooft coupling λ. [ABSTRACT FROM AUTHOR]