Weyl anomalies of four dimensional conformal boundaries and defects

• Published in: The journal of high energy physics 2022-02, Vol.2022 (2), p.166-72, Article 166
• Main Authors: Chalabi, Adam, Herzog, Christopher P., O’Bannon, Andy, Robinson, Brandon, Sisti, Jacopo
• Format: Article
• Language: English
• Subjects: Algorithms; Anomalies; Anomalies in Field and String Theories; Boundary Quantum Field Theory; Classical and Quantum Gravitation; Conformal Field Theory; Defects; Elementary Particles; Fermions; Field Theories in Higher Dimensions; High energy physics; Mathematical analysis; Operators (mathematics); Parity; Physics; Physics and Astronomy; Quantum computing; Quantum entanglement; Quantum Field Theories; Quantum Field Theory; Quantum phenomena; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory; Tensors
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP02(2022)166

A bstract 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.