4,007 research outputs found
Chiral Gauge Theories in the Overlap Formalism
The overlap formula for the chiral determinant is presented and the
realization of gauge anomalies and gauge field toplogy in this context is
discussed. The ability of the overlap formalism to deal with supersymmetric
theories and Majorana-Weyl fermions is outlined. Two applications of the
overlap formalism are discussed in some detail. One application is the
computation of a fermion number violating process in a two dimensional U(1)
chiral gauge theory. The second application is a measurement of the probability
ditribution of the index of the chiral Dirac operator in four dimensional pure
SU(2) lattice gauge theory.Comment: 18 pages, Latex file with six postscript figures incorporated. Talk
given at the "APCTP-ICTP Joint International Conference '97 (AIJIC 97) on
Recent Developments in Non-perturbative Method" held between May 26-30 at
Seoul, Kore
The overlap is not a waveguide
Golterman and Shamir falsely claim that a waveguide model modified by adding
many charged bosonic spinors, in the limit of an infinite number of matter
fields, becomes identical to the overlap if in the target theory every fermion
appears in four copies. Their modified model would give wrong results even in
the vectorial four flavor massless Schwinger model, while a dynamical
simulation of this model with the overlap works correctly. In this note we
pinpoint the error in the derivation of Golterman and Shamir.Comment: Plain Tex, 3 page
Many-flavor Schwinger model at finite chemical potential
We study thermodynamic properties of the Schwinger model on a torus with f
flavors of massless fermions and flavor-dependent chemical potentials.
Generalizing the two-flavor case, we present a representation of the partition
function in the form of a multidimensional theta function and show that the
model exhibits a rich phase structure at zero temperature. The different
phases, characterized by certain values of the particle numbers, are separated
by first-order phase transitions. We work out the phase structure in detail for
three and four fermion flavors and conjecture, based on an exploratory
investigation of the five, six, and eight flavor case, that the maximal number
of coexisting phases at zero temperature grows exponentially with increasing f.Comment: 7 pages, 2 figures, contribution to the 31st International Symposium
on Lattice Field Theory - LATTICE 2013, July 29 - August 3, 2013, Mainz,
German
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