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Summing up all genus free energy of ABJM matrix model

  • Hiroyuki Fuji
  • Shinji Hirano
  • Sanefumi MoriyamaEmail author
Article

Abstract

The localization technique allows us to compute the free energy of the U(N) k  × U(N)k Chern-Simons-matter theory dual to type IIA strings on AdS 4 × CP 3 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 λren.

Keywords

Matrix Models AdS-CFT Correspondence Chern-Simons Theories M-Theory 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Hiroyuki Fuji
    • 1
  • Shinji Hirano
    • 1
  • Sanefumi Moriyama
    • 2
    Email author
  1. 1.Department of PhysicsNagoya UniversityNagoyaJapan
  2. 2.Kobayashi Maskawa InstituteNagoya UniversityNagoyaJapan

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