3d Abelian gauge theories at the boundary

Journal of High Energy Physics

Jingxiang Wu¹  Lorenzo Di Pietro¹  Davide Gaiotto¹  Edoardo Lauria² 

[1] 0000 0000 8658 0851, grid.420198.6, Perimeter Institute for Theoretical Physics, 31 Caroline St N, N2L 2Y5, Waterloo, ON, Canada;0000 0000 8700 0572, grid.8250.f, Centre for Particle Theory, Department of Mathematical Sciences, Durham University, DH1 3LE, Durham, U.K.;

关键词: Boundary Quantum Field Theory;    Chern-Simons Theories;    Conformal Field Theory;    Duality in Gauge Field Theories;   

DOI  :  10.1007/JHEP05(2019)091

来源: publisher

【 摘 要 】

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.

【 授权许可】

Unknown