3d Abelian gauge theories at the boundary
Abstract A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling τ in the upper-half plane and by the choice of the CFT...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2019)091 |
| _version_ | 1818910529437040640 |
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| author | Lorenzo Di Pietro Davide Gaiotto Edoardo Lauria Jingxiang Wu |
| author_facet | Lorenzo Di Pietro Davide Gaiotto Edoardo Lauria Jingxiang Wu |
| author_sort | Lorenzo Di Pietro |
| collection | DOAJ |
| description | Abstract A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling τ in the upper-half plane and by the choice of the CFT in the decoupling limit τ → ∞. Upon performing an SL(2, ℤ) transformation in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten’s SL(2, ℤ) action [1]. In particular the cusps on the real τ axis correspond to the 3d gauging of the original CFT. We study general properties of this BCFT. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. We then consider the case in which the 3d CFT is one Dirac fermion. Thanks to 3d dualities this BCFT is mapped to itself by a bulk S transformation, and it also admits a decoupling limit which gives the O(2) model on the boundary. We compute scaling dimensions of boundary operators and the hemisphere free-energy up to two loops. Using an S-duality improved ansatz, we extrapolate the perturbative results and find good approximations to the observables of the O(2) model. We also consider examples with other theories on the boundary, such as large-N f Dirac fermions — for which the extrapolation to strong coupling can be done exactly order-by-order in 1/N f — and a free complex scalar. |
| first_indexed | 2024-12-19T22:44:15Z |
| format | Article |
| id | doaj.art-f0f5e47f2fd548a5823429666ff44786 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T22:44:15Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f0f5e47f2fd548a5823429666ff447862022-12-21T20:02:59ZengSpringerOpenJournal of High Energy Physics1029-84792019-05-012019516010.1007/JHEP05(2019)0913d Abelian gauge theories at the boundaryLorenzo Di Pietro0Davide Gaiotto1Edoardo Lauria2Jingxiang Wu3Perimeter Institute for Theoretical PhysicsPerimeter Institute for Theoretical PhysicsCentre for Particle Theory, Department of Mathematical Sciences, Durham UniversityPerimeter Institute for Theoretical PhysicsAbstract A four-dimensional Abelian gauge field can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFT) parametrized by the gauge coupling τ in the upper-half plane and by the choice of the CFT in the decoupling limit τ → ∞. Upon performing an SL(2, ℤ) transformation in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten’s SL(2, ℤ) action [1]. In particular the cusps on the real τ axis correspond to the 3d gauging of the original CFT. We study general properties of this BCFT. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. We then consider the case in which the 3d CFT is one Dirac fermion. Thanks to 3d dualities this BCFT is mapped to itself by a bulk S transformation, and it also admits a decoupling limit which gives the O(2) model on the boundary. We compute scaling dimensions of boundary operators and the hemisphere free-energy up to two loops. Using an S-duality improved ansatz, we extrapolate the perturbative results and find good approximations to the observables of the O(2) model. We also consider examples with other theories on the boundary, such as large-N f Dirac fermions — for which the extrapolation to strong coupling can be done exactly order-by-order in 1/N f — and a free complex scalar.http://link.springer.com/article/10.1007/JHEP05(2019)091Boundary Quantum Field TheoryChern-Simons TheoriesConformal Field TheoryDuality in Gauge Field Theories |
| spellingShingle | Lorenzo Di Pietro Davide Gaiotto Edoardo Lauria Jingxiang Wu 3d Abelian gauge theories at the boundary Journal of High Energy Physics Boundary Quantum Field Theory Chern-Simons Theories Conformal Field Theory Duality in Gauge Field Theories |
| title | 3d Abelian gauge theories at the boundary |
| title_full | 3d Abelian gauge theories at the boundary |
| title_fullStr | 3d Abelian gauge theories at the boundary |
| title_full_unstemmed | 3d Abelian gauge theories at the boundary |
| title_short | 3d Abelian gauge theories at the boundary |
| title_sort | 3d abelian gauge theories at the boundary |
| topic | Boundary Quantum Field Theory Chern-Simons Theories Conformal Field Theory Duality in Gauge Field Theories |
| url | http://link.springer.com/article/10.1007/JHEP05(2019)091 |
| work_keys_str_mv | AT lorenzodipietro 3dabeliangaugetheoriesattheboundary AT davidegaiotto 3dabeliangaugetheoriesattheboundary AT edoardolauria 3dabeliangaugetheoriesattheboundary AT jingxiangwu 3dabeliangaugetheoriesattheboundary |