The functional bootstrap for boundary CFT

• Main Authors: Apratim Kaviraj, Miguel F. Paulos
• Format: Article
• Language: English
• Published: SpringerOpen 2020-04-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Theory; Nonperturbative Effects; AdS-CFT Correspondence
• Online Access: http://link.springer.com/article/10.1007/JHEP04(2020)135

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 ϵ 2.