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Register a new userThe Effect of Dynamical Gauge Field on the Chiral Fermion on a boundary
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We study the effect of dynamical gauge field on the Kaplans chiral fermion on a boundary in the strong gauge coupling limit in the extra dimension. To all orders of the hopping parameter expansion, we prove exact parity invariance of the fermion propagator on the boundary. This means that the chiral property of the boundary fermion, which seems to survive even in the presence of the gauge field from a perturbative point of view, is completely destroyed by the dynamics of the gauge field.
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We only require generalized chiral symmetry and $gamma_5$-hermiticity, which leads to a large class of Dirac operators describing massless fermions on the lattice, and use this framework to give an overview of developments in this field. Spectral representations turn out to be a powerful tool for obtaining detailed properties of the operators and a general construction of them. A basic unitary operator is seen to play a central r^ole in this context. We discuss a number of special cases of the operators and elaborate on various aspects of index relations. We also show that our weaker conditions lead still properly to Weyl fermions and to chiral gauge theories.
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The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. Since this ensemble implies a projection to the zero triality sector of the theory we introduce a proper quantity which is able to reveal a critical behaviour of the theory with fundamental quarks. We discuss the properties of both the chromoelectric and chromomagnetic sectors of the theory and show while electric charges carrying a unit of Z(N) charge are screened at high temperatures by dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local discrete Z(N) symmetry in the magnetic sector. We argue it can be used to detect a deconfinement phase being defined in terms of the screening mechanism as a phase of unscreened Z(N) flux. It may be detectable at long range via the Aharonov-Bohm effect. We discuss the possible phase structure of QCD in this approach.
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