Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects

Abstract

Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension $d\ge 5$ 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 $d\ge 6$; and Takayanagi's AdS/BCFT with $d=5$. We demonstrate that several of our examples obey the boundary/defect $a$-theorem, as expected.

arXiv comment1+73 pages, 7 figures, 1 ancillary Mathematica notebook; v2: references and clarifying footnote added, typos corrected, published in JHEP; v3: additional references added

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