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Using 2-d U(1) lattice gauge theory we study two definitions of the topological charge constructed from a generalized Villain action and analyze the implementation of the index theorem based on the overlap Dirac operator. One of the two definitions expresses the topological charge as a sum of the Villain variables and treats charge conjugation symmetry exactly, making it particularly useful for studying related physics. Our numerical analysis establishes that for both topological charge definitions the index theorem becomes exact quickly towards the continuum limit.
We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $eta$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a fi
We give a prescription for how to compute the Callias index, using as regulator an exponential function. We find agreement with old results in all odd dimensions. We show that the problem of computing the dimension of the moduli space of self-dual st
We perform a numerical test of a relativistic heavy quark(RHQ) action, recently proposed by Tsukuba group, in quenched lattice QCD at $asimeq 0.1$ fm. With the use of the improvement parameters previously determined at one-loop level for the RHQ acti
We study lattice QCD with a gauge action, which suppresses small plaquette values. Thus the MC history is confined to a single topological sector over a significant time, while other observables are decorrelated. This enables the cumulation of statis
A way to identify the would-be zero-modes of staggered lattice fermions away from the continuum limit is presented. Our approach also identifies the chiralities of these modes, and their index is seen to be determined by gauge field topology in accor