2014/05/02 by Mario Kieburg, J. J. M. Verbaarschot, Jacobus J. M. Verbaarschot +1
Mathematics · Physics and Astronomy · #Chiral perturbation theory #Eigenvalues and eigenvectors #Geometry #Homogeneous space #Lattice QCD #Lattice field theory #Mathematical physics #Mathematics #Particle physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum many-body systems #Quantum mechanics #Quark #Random matrix #Spectral line #Theoretical physics #Topological Materials and Phenomena #cond-mat.dis-nn #hep-lat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.90.085013
published as Phys. Rev. D 90, 085013 (2014)
arxiv created 2014/05/02 · openalex publication_date 2014/10/15 · arxiv updated 2014/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \ensuremathγ5. 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.