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Abstract |
A four-dimensional abelian gauge theory 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 (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT
in the decoupling limit. Upon performing an Electric-Magnetic duality 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. In particular the cusps on the real \tau axis
correspond to the 3d gauging of the original CFT. We study general properties of this family of
BCFTs. 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.
Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn
this machinery into a powerful computational tool to study 3d gauge theories. |
