Chiral Lattice Fermions, Minimal Doubling, and the Axial Anomaly

Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from non-conservation of the flavor-singlet current. Similar non-conservation also leads to the axial anomaly in the case of the naive lattice action. For minimally doubled actions, however, fine tuning of the action and axial current is necessary to arrive at the anomaly. Conservation of the flavor non-singlet vector current additionally requires the current to be fine tuned. Finally we determine that the chiral projection of a minimally doubled fermion action can be used to arrive at a lattice theory with an undoubled Dirac fermion possessing the correct anomaly in the continuum limit.Comment: 15 pages, 1 figure, symmetries corrected, Symanzik analysis for currents added, marginal operators expose

Quarks with Twisted Boundary Conditions in the Epsilon Regime

We study the effects of twisted boundary conditions on the quark fields in the epsilon regime of chiral perturbation theory. We consider the $SU(2)_L\times SU(2)_R$ chiral theory with non-degenerate quarks and the $SU(3)_L\times SU(3)_R$ chiral theory with massless up and down quarks and massive strange quarks. The partition function and condensate are derived for each theory. Because flavor-neutral Goldstone bosons are unaffected by twisted boundary conditions chiral symmetry is still restored in finite volumes. The dependence of the condensate on the twisting parameters can be used to extract the pion decay constant from simulations in the epsilon regime. The relative contribution to the partition function from sectors of different topological charge is numerically insensitive to twisted boundary conditions.Comment: 15 pages, 4 figure

Time Dependence of Nucleon Correlation Functions in Chiral Perturbation Theory

We consider corrections to nucleon correlation functions arising from times that are far from the asymptotic limit. For such times, the single nucleon state is contaminated by the pion-nucleon and pion-delta continuum. We use heavy baryon chiral perturbation theory to derive the spectral representation of the nucleon two-point function. Finite time corrections to the axial current correlation function are also derived. Pion-nucleon excited state contributions drive the axial correlator upward, while contributions from the interference of pion-delta and pion-nucleon states drive the axial correlator downward. Our results can be compared qualitatively to optimized nucleon correlators calculated in lattice QCD, because the chiral corrections characterize only low-energy excitations above the ground state. We show that improved nucleon operators can lead to an underestimation of the nucleon axial charge.Comment: 12 pages, 4 figure