Journal article
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 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-Nf Dirac fermions — for which the extrapolation to strong coupling can be done exactly order-by-order in 1/Nf — and a free complex scalar.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.6MB, Terms of use)
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- Publisher copy:
- 10.1007/JHEP05(2019)091
Authors
- Publisher:
- Springer
- Journal:
- Journal of High Energy Physics More from this journal
- Volume:
- 2019
- Issue:
- 5
- Article number:
- 91
- Publication date:
- 2019-05-17
- Acceptance date:
- 2019-04-24
- DOI:
- EISSN:
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1029-8479
- ISSN:
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1126-6708
- Language:
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English
- Keywords:
- Pubs id:
-
1189946
- Local pid:
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pubs:1189946
- Deposit date:
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2021-08-21
- ARK identifier:
Terms of use
- Copyright holder:
- Di Pietro et al.
- Copyright date:
- 2019
- Rights statement:
- Copyright © 2019, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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