Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects

Authors: Adam Chalabi, Christopher P. Herzog, Andy O'Bannon, Brandon Robinson, Jacopo Sisti

Preprint number: UUITP-58/21

Abstract: Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformally-invariant spatial boundary (BCFTs) or 4-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT's Weyl tensor. For a co-dimension one boundary or defect (i.e. d=5), we reproduce the 9 parity-even terms found by Astaneh and Solodukhin, and we discover 3 parity-odd terms. For larger co-dimension, we find 23 parity-even terms and 6 parity-odd terms. The coefficient of each term defines a "central charge" that characterizes the BCFT or DCFT. We show how several of the parity-even central charges enter physical observables, namely the displacement operator two-point function, the stress-tensor one-point function, and the universal part of the entanglement entropy. We compute several parity-even central charges in tractable examples:  monodromy and conical defects of free, massless scalars and Dirac fermions in d=6; probe branes in Anti-de Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi's AdS/BCFT with d=5. We demonstrate that several of our examples obey the boundary/defect a-theorem, as expected.