Self-dual U(1) lattice field theory with a θ-term

Anosova, Mariia; Gattringer, Christof; Sulejmanpasic, Tin

Abstract

We study U(1) gauge theories with a modified Villain action. Such theories can naturally be coupled to electric and magnetic matter, and display exact electric-magnetic duality. In their simplest formulation without a θ-term, such theories are ultra-local. We extend the discussion to U(1) gauge theories with θ-terms, such that θ periodicity is exact for a free theory, and show that imposing electric-magnetic duality results in a local, but not ultra-local lattice action, which is reminiscent of the Lüscher construction of axial- symmetry preserving fermions in 4d. We discuss the coupling to electric and magnetic matter as well as to dyons. For dyonic matter the electric-magnetic duality and shifts of the θ-angle by 2π together generate an SL(2, ℤ) duality group of transformations, just like in the continuum. We finally illustrate how the SL(2, ℤ) duality may be used to explore theories at finite θ without a sign problem.

Citation

Anosova, M., Gattringer, C., & Sulejmanpasic, T. (2022). Self-dual U(1) lattice field theory with a θ-term. Journal of High Energy Physics, 2022(4), Article 120. https://doi.org/10.1007/jhep04%282022%29120

• Journal Article Type: Article
• Acceptance Date: Mar 23, 2022
• Online Publication Date: Apr 21, 2022
• Publication Date: 2022-04
• Deposit Date: Jul 5, 2022
• Publicly Available Date: Jul 5, 2022
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Issue: 4
• Article Number: 120
• DOI: https://doi.org/10.1007/jhep04%282022%29120
• Public URL: https://durham-repository.worktribe.com/output/1199757