Masazumi Honda

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

A bstractWe show that the ABJM theory, which is an

Supersymmetry non-renormalization theorem from a computer and the AdS/CFT correspondence

\mathcal{N} = {6}

Testing the AdS/CFT correspondence by Monte Carlo calculation of BPS and non-BPS Wilson loops in N=4 super-Yang-Mills theory

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 N3/2 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.

Testing the AdS/CFT correspondence by Monte Carlo calculation of BPS and non-BPS Wilson loops in 4d N=4 super-Yang-Mills theory

We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which reduces the calculation to that of corresponding correlation functions in the plane-wave matrix model or the BMN matrix model. This model is a 1d gauge theory with 16 supersymmetries, which can be simulated in a manner similar to the recent studies of the D0-brane system. We study two-point and three-point functions of chiral primary operators at various coupling constant, and find that they agree with the free theory results up to overall constant factors. The ratio of the overall factors for two-point and three-point functions agrees with the prediction of the AdS/CFT correspondence.

Supersymmetric index on T^2 x S^2 and elliptic genus

We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R×S3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a track-shaped Wilson loop from the gravity side, which shows that a clear test of the AdS/CFT for the non-BPS case is also feasible.

Monte Carlo studies of 3d N=6 SCFT via localization method

We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R×S3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a track-shaped Wilson loop from the gravity side, which shows that a clear test of the AdS/CFT for the non-BPS case is also feasible.