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

Anosova, Mariia; Gattringer, Christof; Sulejmanpasic, Tin

doi:10.1007/jhep04(2022)120

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

Anosova, Mariia; Gattringer, Christof; Sulejmanpasic, Tin

Authors

Mariia Anosova

Christof Gattringer

Dr Tin Sulejmanpasic tin.sulejmanpasic@durham.ac.uk
Associate Professor

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
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

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