Topological terms in abelian lattice field theories

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

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, December). Topological terms in abelian lattice field theories. Presented at Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

• Presentation Conference Type: Conference Paper (published)
• 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
• Public URL: https://durham-repository.worktribe.com/output/1134724