Correlation between Polyakov loops oriented in two different directions in SU(N) gauge theory on a two-dimensional torus

Joe Kiskis, Rajamani Narayanan, and Dibakar Sigdel
Phys. Rev. D 89, 085031 – Published 16 April 2014

Abstract

We consider SU(N) gauge theories on a two-dimensional torus with finite area, A. Let Tμ(A) denote the Polyakov loop operator in the μ direction. Starting from the lattice gauge theory on the torus, we derive a formula for the continuum limit of g1(T1(A))g2(T2(A)) as a function of the area of the torus where g1 and g2 are class functions. We show that there exists a class function ξ0 for SU(2) such that ξ0(T1(A))ξ0(T2(A))>1 for all finite area of the torus with the limit being unity as the area of the torus goes to infinity. Only the trivial representation contributes to ξ0 as A whereas all representations become equally important as A0.

  • Figure
  • Figure
  • Received 12 March 2014

DOI:https://doi.org/10.1103/PhysRevD.89.085031

© 2014 American Physical Society

Authors & Affiliations

Joe Kiskis*

  • Department of Physics, University of California, Davis, California 95616, USA

Rajamani Narayanan and Dibakar Sigdel

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

  • *jekiskis@ucdavis.edu
  • rajamani.narayanan@fiu.edu
  • dibakar.sigdel@fiu.edu

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Issue

Vol. 89, Iss. 8 — 15 April 2014

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