Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills Theory

Abstract

We study spontaneous chiral symmetry breaking and the spectral properties of the staggered lattice Dirac operator using quenched gauge configurations for the exceptional group G2, which has a trivial center. In particular we study the system below and above the finite temperature transition and use the temporal boundary conditions of the fermions to probe the system. We evaluate several observables: The spectral density at the origin, the spectral gap, the chiral condensate and the recently proposed dual chiral condensate. We show that chiral symmetry is broken at low temperatures and is restored at high temperatures at the thermodynamic phase transition. Concerning the role of the boundary conditions we establish that in all respects the spectral quantities behave for G2 in exactly the same way as for SU(N), when for the latter group the gauge ensemble above T_c is restricted to the sector of configurations with real Polyakov loop.

arXiv commentMinor modifications, version to appear in JHEP

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• Exceptional thermodynamics: The equation of state of G(2) gauge theory
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• On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators
• Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories
• Topology and $\theta$ dependence in finite temperature $G_2$ lattice gauge theory
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• Topological aspects of G2 Yang-Mills theory
• Effective Polyakov Loop Dynamics for Finite Temperature G(2) Gluodynamics
• On the Landau-gauge adjoint quark propagator
• Constructing a neutron star in G2-QCD
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• The quark propagator in QCD and $G_2$ QCD
• Remarks on the Confinement in the $G(2)$ Gauge Theory Using the Thick Center Vortex Model
• Lattice simulations of $G_2$-QCD at finite density