Summing Up All Genus Free Energy of ABJM Matrix Model
High Energy Physics - Theory
2011-08-03 v2
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 \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.
Keywords
Cite
@article{arxiv.1106.4631,
title = {Summing Up All Genus Free Energy of ABJM Matrix Model},
author = {Hiroyuki Fuji and Shinji Hirano and Sanefumi Moriyama},
journal= {arXiv preprint arXiv:1106.4631},
year = {2011}
}
Comments
18 pages, no figures, v2: typos corrected and references added