85 research outputs found
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
chiral theory with non-degenerate quarks and the
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
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