PoS - Proceedings of Science
Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Topological terms in abelian lattice field theories
C. Gattringer*, M. Anosova, D. Göschl, T. Sulejmanpasic and P. Törek
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Pre-published on: January 04, 2020
Published on: August 27, 2020
In this contribution we revisit the lattice discretization of the topological charge for abelian lattice field theories. The construction departs from an initially non-compact discretization of the gauge fields and after absorbing $2\pi$ shifts of the gauge fields leads to a generalized Villain action that also includes the topological term. The topological charge in two, as well as in four dimensions can be expressed in terms of only the integer-valued Villain variables. We test various properties of the topological charge and in particular analyze the index theorem in two dimensions and discuss the Witten effect in 4-d. As an application of our formulation we present results from a simulation of the 2-d U(1) gauge Higgs model at vacuum angle $\theta = \pi$, where we use a suitable worldline/worldsheet representation to overcome the complex action problem at non-zero $\theta$.
DOI: https://doi.org/10.22323/1.363.0082
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