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

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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.

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Authors and Affiliations

  1. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, 305-0801, Japan

    Masanori Hanada, Jun Nishimura, Shotaro Shiba & Yutaka Yoshida

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, U.S.A.

    Masanori Hanada, Masazumi Honda & Jun Nishimura

  3. Department of Particle and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI), Tsukuba, Ibaraki, 305-0801, Japan

    Masazumi Honda, Yoshinori Honma & Jun Nishimura

  4. Blackett Laboratory, Imperial College London, London, SW7 2AZ, U.K.

    Shotaro Shiba

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  1. Masanori Hanada
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  2. Masazumi Honda
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  3. Yoshinori Honma
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  4. Jun Nishimura
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Correspondence to Masazumi Honda.

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ArXiv ePrint: 1202.5300

The simulation code is available upon request to mhonda@post.kek.jp.

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Hanada, M., Honda, M., Honma, Y. et al. Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant. J. High Energ. Phys. 2012, 121 (2012). https://doi.org/10.1007/JHEP05(2012)121

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