Dirac spectra of two-dimensional QCD-like theories

Mario Kieburg, Jacobus J. M. Verbaarschot, and Savvas Zafeiropoulos
Phys. Rev. D 90, 085013 – Published 15 October 2014

Abstract

We analyze Dirac spectra of two-dimensional QCD-like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is different from QCD in four dimensions because the antiunitary symmetries do not commute with γ5. Therefore, in a chiral basis, the number of degrees of freedom per matrix element are not given by the Dyson index. Our predictions are confirmed by Dirac spectra from quenched lattice simulations for QCD with two or three colors with quarks in the fundamental representation as well as in the adjoint representation. The universality class of the spectra depends on the parity of the number of lattice points in each direction. Our results show an agreement with random matrix theory that is qualitatively similar to the agreement found for QCD in four dimensions. We discuss the implications for the Mermin-Wagner-Coleman theorem and put our results in the context of two-dimensional disordered systems.

  • Figure
  • Figure
  • Figure
  • Received 9 May 2014

DOI:https://doi.org/10.1103/PhysRevD.90.085013

© 2014 American Physical Society

Authors & Affiliations

Mario Kieburg1,2,*, Jacobus J. M. Verbaarschot1,†, and Savvas Zafeiropoulos1,3,‡

  • 1Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
  • 2Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
  • 3Laboratoire de Physique Corpusculaire, Université Blaise Pascal, CNRS/IN2P3, 63177 Aubière Cedex, France

  • *mkieburg@physik.uni-bielefeld.de
  • jacobus.verbaarschot@stonybrook.edu
  • zafeiropoulos@clermont.in2p3.fr

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 8 — 15 October 2014

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×