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The functional bootstrap for boundary CFT
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DOI：10.1007/JHEP04(2020)135.png)
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Abstract
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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 E-expansion to order E-2.
Keywords:
Conformal Field Theory
Nonperturbative Effects
AdS-CFT Correspondence
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