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arXiv · 1106.4631

Summing Up All Genus Free Energy of ABJM Matrix Model

Hiroyuki Fuji·Shinji Hirano·Sanefumi Moriyama
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Abstract

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 λ= 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} λ_r), with the renormalized 't Hooft coupling λ_r.

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Hiroyuki Fuji, Shinji Hirano, Sanefumi Moriyama. 2011-07-13. Summing Up All Genus Free Energy of ABJM Matrix Model. https://doi.org/10.1007/jhep08(2011)001

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