Abstract
We introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear functionals which act on the crossing equation to give a set of sum rules on the boundary CFT data: the functional bootstrap equations. We show these equations are essentially equivalent to a Polyakov-type approach to the bootstrap of BCFTs, and show how to fix the so-called contact term ambiguity in that context. Finally, the functional bootstrap equations diagonalize perturbation theory around generalized free fields, which we use to recover the Wilson-Fisher BCFT data in the ϵ-expansion to order ϵ2.
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Kaviraj, A., Paulos, M.F. The functional bootstrap for boundary CFT. J. High Energ. Phys. 2020, 135 (2020). https://doi.org/10.1007/JHEP04(2020)135
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DOI: https://doi.org/10.1007/JHEP04(2020)135