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Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion

A. Hietanen and R. Narayanan
Phys. Rev. D 86, 085002 – Published 1 October 2012
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  • INTRODUCTION
  • THE MODEL
  • THE NUMERICAL ALGORITHM
  • OPERATORS
  • SINGLE SITE MODEL WITH MASSLESS ADJOINT…
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    We use a single site lattice in four dimensions to study the scaling of large N Yang-Mills field coupled to a single massless Dirac fermion in the adjoint representation. We use the location of the strong to the weak coupling transition defined through the eigenvalues of the folded Wilson loop operator to set a scale. We do not observe perturbative scaling in the region studied in this paper. Instead, we observe that the scale changes very slowly with the bare coupling. The lowest eigenvalue of the overlap Dirac operator is another scale that shows similar behavior as a function of the lattice coupling.

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    • Received 16 July 2012

    DOI:https://doi.org/10.1103/PhysRevD.86.085002

    © 2012 American Physical Society

    Authors & Affiliations

    A. Hietanen*

    • CP3-Origins and the Danish Institute for Advanced Study DIAS, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

    R. Narayanan†

    • Department of Physics, Florida International University, Miami, Florida 33199, USA

    • *hietanen@cp3-origins.net
    • †rajamani.narayanan@fiu.edu

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    Vol. 86, Iss. 8 — 15 October 2012

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    Images

    • Figure 1
      Figure 1
      Average value of the plaquette along with the average values for the four different Polyakov loop observables for massless fermions at N=18.Reuse & Permissions
    • Figure 2
      Figure 2
      Running of the tadpole-improved coupling versus the logarithmic scale lna(b) for massless fermions at N=18.Reuse & Permissions
    • Figure 3
      Figure 3
      Running of the tadpole-improved coupling versus the logarithmic scale lnλ(b) for massless fermions at N=18.Reuse & Permissions
    • Figure 4
      Figure 4
      Plot of the quantity, Ω(L,N,b), as a function of L−1 at N=18 and b=0.55 for massless fermions. The (red) square is the estimate listed in Table .Reuse & Permissions
    • Figure 5
      Figure 5
      The distribution of the eigenvalues of the square Wilson loop operators for three different sizes at N=18 and b=0.32 with massless fermions.Reuse & Permissions
    • Figure 6
      Figure 6
      The full distribution of the eigenvalues of the massless adjoint overlap Dirac operator for three different couplings at N=18.Reuse & Permissions
    • Figure 7
      Figure 7
      The ratios of the eigenvalues of the massless adjoint overlap Dirac operator are shown in log-log plot for all the data listed in Table .Reuse & Permissions
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