Masanori Hanada, Masazumi Honda, Yoshinori Honma, Jun Nishimura, Shotaro Shiba, Yutaka Yoshida
We show that the ABJM theory, which is a N=6 superconformal U(N)\times 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 AdS_4/CFT_3 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 the previously proposed analytical formula needs to be corrected by an additional term at each order of the string coupling 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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http://arxiv.org/abs/1202.5300
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