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Journal of High Energy Physics

, 2013:200 | Cite as

Direct test of the AdS/CFT correspondence by Monte Carlo studies of \( \mathcal{N}=4 \) super Yang-Mills theory

  • Masazumi Honda
  • Goro Ishiki
  • Sang-Woo KimEmail author
  • Jun Nishimura
  • Asato Tsuchiya
Article
First Online:

Abstract

We perform nonperturbative studies of \( \mathcal{N}=4 \) 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 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 \( \mathcal{N}=4 \) SU(N) theory on R × S 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 for S 3 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 Λ in R direction, are made negligible by using sufficiently large Λ.

Keywords

AdS-CFT Correspondence Supersymmetric gauge theory Matrix Models 
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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Masazumi Honda
    • 1
    • 2
    • 3
  • Goro Ishiki
    • 2
    • 3
    • 4
  • Sang-Woo Kim
    • 2
    • 4
    • 5
    • 6
    Email author
  • Jun Nishimura
    • 1
    • 2
  • Asato Tsuchiya
    • 7
  1. 1.Department of Particle and Nuclear PhysicsGraduate University for Advanced Studies (SOKENDAI)TsukubaJapan
  2. 2.High Energy Accelerator Research Organization (KEK)TsukubaJapan
  3. 3.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  4. 4.Center for Quantum Spacetime (CQUeST)Sogang UniversitySeoulKorea
  5. 5.Department of PhysicsOsaka UniversityToyonakaJapan
  6. 6.School of Physics, Korea Institute for Advanced StudySeoulKorea
  7. 7.Department of PhysicsShizuoka UniversityShizuokaJapan

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