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Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant

  • Masanori Hanada
  • Masazumi HondaEmail author
  • Yoshinori Honma
  • Jun Nishimura
  • Shotaro Shiba
  • Yutaka Yoshida
Article

Abstract

We show that the ABJM theory, which is an \( \mathcal{N} = {6} \) superconformal U(N) × U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived from the theory by using the localization technique. This opens up the possibility of probing the quantum aspects of M-theory and testing the AdS4/CFT3 duality at the quantum level. Here we calculate the free energy, and confirm the N 3/2 scaling in the M-theory limit predicted from the gravity side. We also find that our results nicely interpolate the analytical formulae proposed previously in the M-theory and type IIA regimes. Furthermore, we show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion. The method can be easily generalized to the calculations of BPS operators and to other theories that reduce to matrix models.

Keywords

Gauge-gravity correspondence AdS-CFT Correspondence M-Theory 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Masanori Hanada
    • 1
    • 2
  • Masazumi Honda
    • 2
    • 3
    Email author
  • Yoshinori Honma
    • 3
  • Jun Nishimura
    • 1
    • 2
    • 3
  • Shotaro Shiba
    • 1
    • 4
  • Yutaka Yoshida
    • 1
  1. 1.High Energy Accelerator Research Organization (KEK)TsukubaJapan
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.
  3. 3.Department of Particle and Nuclear PhysicsGraduate University for Advanced Studies (SOKENDAI)TsukubaJapan
  4. 4.Blackett LaboratoryImperial College LondonLondonU.K.

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