Self-dual U(1) lattice field theory with a θ-term
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) g...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2022)120 |
| _version_ | 1797865810213994496 |
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| author | Mariia Anosova Christof Gattringer Tin Sulejmanpasic |
| author_facet | Mariia Anosova Christof Gattringer Tin Sulejmanpasic |
| author_sort | Mariia Anosova |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T23:13:44Z |
| format | Article |
| id | doaj.art-08a10ad38c2f472d8a36597f9e5573b3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:13:44Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-08a10ad38c2f472d8a36597f9e5573b32023-03-22T10:10:36ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022414510.1007/JHEP04(2022)120Self-dual U(1) lattice field theory with a θ-termMariia Anosova0Christof Gattringer1Tin Sulejmanpasic2Institut für Physik, Universität GrazFWF — Austrian Science FundDepartment of Mathematical Sciences, Durham UniversityAbstract 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.https://doi.org/10.1007/JHEP04(2022)120Duality in Gauge Field TheoriesLattice Quantum Field Theory |
| spellingShingle | Mariia Anosova Christof Gattringer Tin Sulejmanpasic Self-dual U(1) lattice field theory with a θ-term Journal of High Energy Physics Duality in Gauge Field Theories Lattice Quantum Field Theory |
| title | Self-dual U(1) lattice field theory with a θ-term |
| title_full | Self-dual U(1) lattice field theory with a θ-term |
| title_fullStr | Self-dual U(1) lattice field theory with a θ-term |
| title_full_unstemmed | Self-dual U(1) lattice field theory with a θ-term |
| title_short | Self-dual U(1) lattice field theory with a θ-term |
| title_sort | self dual u 1 lattice field theory with a θ term |
| topic | Duality in Gauge Field Theories Lattice Quantum Field Theory |
| url | https://doi.org/10.1007/JHEP04(2022)120 |
| work_keys_str_mv | AT mariiaanosova selfdualu1latticefieldtheorywithathterm AT christofgattringer selfdualu1latticefieldtheorywithathterm AT tinsulejmanpasic selfdualu1latticefieldtheorywithathterm |