The Functional Bootstrap for Boundary CFT

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 $\epsilon$-expansion to order ${\epsilon }^2$.

arXiv comment57 Pages, 4 figures, references, minor corrections and some details added

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Cited by in corpus (4)

• Dispersion relations and exact bounds on CFT correlators
• A Basis of Analytic Functionals for CFTs in General Dimension
• Composite operators near the boundary
• Positive geometry in the diagonal limit of the conformal bootstrap