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Topological terms in abelian lattice field theories

Gattringer, Christof; Anosova, Mariia; Göschl, Daniel; Sulejmanpasic, Tin; Törek, Pascal

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Authors

Christof Gattringer

Mariia Anosova

Daniel Göschl

Pascal Törek



Abstract

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 2π 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 θ=π, where we use a suitable worldline/worldsheet representation to overcome the complex action problem at non-zero θ.

Citation

Gattringer, C., Anosova, M., Göschl, D., Sulejmanpasic, T., & Törek, P. (2020). Topological terms in abelian lattice field theories. . https://doi.org/10.22323/1.363.0082

Conference Name Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)
Acceptance Date Jan 4, 2020
Online Publication Date Aug 27, 2020
Publication Date 2020
Deposit Date Oct 28, 2022
Publicly Available Date Oct 28, 2022
Publisher Sissa Medialab
DOI https://doi.org/10.22323/1.363.0082

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