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

• Published in: The journal of high energy physics 2022-04, Vol.2022 (4), p.120-45, Article 120
• Main Authors: Anosova, Mariia, Gattringer, Christof, Sulejmanpasic, Tin
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Duality in Gauge Field Theories; Elementary Particles; Fermions; Field theory; Gauge theory; High energy physics; Lattice Quantum Field Theory; Lattice theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2022)120

A bstract 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 2 π 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.