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Journal of High Energy Physics

, 2011:36 | Cite as

Perturbative tests for a large-N reduced model of \( \mathcal{N} = {4} \) super Yang-Mills theory

  • Goro Ishiki
  • Shinji ShimasakiEmail author
  • Asato Tsuchiya
Article
First Online:

Abstract

We study a non-perturbative formulation of \( \mathcal{N} = {4} \) super Yang-Mills theory (SYM) on R × S 3 in the planar limit proposed in arXiv:0807.2352. This formulation is based on the large-N reduction, and the theory can be described as a particular large-N limit of the plane wave matrix model (PWMM), which is obtained by dimensionally reducing the original theory over S 3. In this paper, we perform some tests for this proposal. We construct an operator in the PWMM that corresponds to the Wilson loop in SYM in the continuum limit and calculate the vacuum expectation value of the operator for the case of the circular contour. We find that our result indeed agrees with the well-known result first obtained by Erickson, Semenoff and Zarembo. We also compute the beta function at the 1-loop level based on this formulation and see that it is indeed vanishing.

Keywords

Supersymmetric gauge theory AdS-CFT Correspondence Non-Commutative Geometry M(atrix) Theories 
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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Goro Ishiki
    • 1
    • 2
  • Shinji Shimasaki
    • 2
    • 3
    Email author
  • Asato Tsuchiya
    • 4
  1. 1.Center for Quantum Spacetime (CQUeST)Sogang UniversitySeoulRepublic of Korea
  2. 2.Department of PhysicsKyoto UniversityKyotoJapan
  3. 3.Harish-Chandra Research InstituteAllahabadIndia
  4. 4.Department of PhysicsShizuoka UniversityShizuokaJapan

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