Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory

Abstract

We perform nonperturbative studies of N=4 super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but \emph{not} by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large-N limit between the N=4 SU(N) theory on RxS^3 and a one-dimensional SU(N) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large-N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff $\Lambda$ in R direction, are made negligible by using sufficiently large $\Lambda$.

v1) 39 pages, 12 figures; v2) references added; v3) published version with minor corrections

References in corpus (29)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Volume independence in large Nc QCD-like gauge theories
• Precision holography for non-conformal branes
• Black hole thermodynamics from simulations of lattice Yang-Mills theory
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Non-lattice simulation for supersymmetric gauge theories in one dimension
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• N=4 Super Yang-Mills from the Plane Wave Matrix Model
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 from supersymmetric matrix quantum mechanics
• Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Testing a novel large-N reduction for N=4 super Yang-Mills theory on RxS^3
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• First Results from Lattice Simulation of the PWMM
• Fiber Bundles and Matrix Models
• Lattice four-dimensional N=4 SYM is practical
• First results from simulations of supersymmetric lattices
• Twisted supersymmetries in lattice $\mathcal{N}=4$ super Yang-Mills theory
• Some Implications of Perturbative Approach to AdS/CFT Correspondence
• Numerical tests of AdS/CFT at strong coupling
• Large N reduction for Chern-Simons theory on S^3
• A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory
• AdS/CFT Correspondence as a Consequence of Scale Invariance
• Large N reduction on coset spaces
• Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature
• Supersymmetry non-renormalization theorem from a computer and the AdS/CFT correspondence
• One dimensional supersymmetric Yang-Mills theory with 16 supercharges
• The shape of emergent quantum geometry from an N=4 SYM minisuperspace approximation

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• The non-perturbative phase diagram of the BMN matrix model
• Real space renormalization group for twisted lattice N=4 super Yang-Mills
• Progress and prospects of lattice supersymmetry
• Lifting flat directions in lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface
• On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
• Loop formulation of supersymmetric Yang-Mills quantum mechanics
• Green-Schwarz superstring on the lattice
• S-duality invariant perturbation theory improved by holography
• A Euclidean Lattice Formulation of D=5 Maximally Supersymmetric Yang-Mills Theory
• QCD, with Strings Attached
• On regularizing the AdS superstring worldsheet
• Emergent Geometries from the BMN Matrix Model