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3d Abelian gauge theories at the boundary

Di Pietro, Lorenzo; Gaiotto, Davide; Lauria, Edoardo; Wu, Jingxiang

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Lorenzo Di Pietro

Davide Gaiotto

Edoardo Lauria

Jingxiang Wu


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.


Di Pietro, L., Gaiotto, D., Lauria, E., & Wu, J. (2019). 3d Abelian gauge theories at the boundary. Journal of High Energy Physics, 2019(5), Article 91.

Journal Article Type Article
Acceptance Date Apr 24, 2019
Online Publication Date May 17, 2019
Publication Date May 31, 2019
Deposit Date May 29, 2019
Publicly Available Date May 29, 2019
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2019
Issue 5
Article Number 91


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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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