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