Summing Up All Genus Free Energy of ABJM Matrix Model

Details Summing Up All Genus Free Energy of ABJM Matrix Model Summing Up All Genus Free Energy of ABJM Matrix Model

2011-06-23

arxiv.org/abs/1106.4631v2

JHEP 1108:001,2011

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, no figures, v2: typos corrected and references added

Scientific paper

10.1007/JHEP08(2011)001

The localization technique allows us to compute the free energy of the U(N)_k x U(N)_{-k} Chern-Simons-matter theory dual to type IIA strings on AdS_4 x CP^3 from weak to strong 't Hooft coupling \lambda = N / k at finite N, as demonstrated by Drukker, Marino, 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 all the 1/N corrections, apart from the worldsheet instanton contributions. The all genus partition function takes a remarkably simple form -- the Airy function, Ai (k^{4/3} \lambda_r), with the renormalized 't Hooft coupling \lambda_r.

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