3d Abelian gauge theories at the boundary

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

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.

Citation

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. https://doi.org/10.1007/jhep05%282019%29091

• 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
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2019
• Issue: 5
• Article Number: 91
• DOI: https://doi.org/10.1007/jhep05%282019%29091
• Public URL: https://durham-repository.worktribe.com/output/1300922