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.
Highlights
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
What information characterizes a Quantum Field Theory (QFT) uniquely? Can we use this information to classify QFTs, or map the space of QFTs? Can we prove that this information must obey constraints, eliminating regions in the space of QFTs? These questions are vitally important for many areas of physics
We show how two of the defect central charges appear in the universal contribution to entanglement entropy (EE) of a spherical region centered on the defect [30, 36], and how the Average Null Energy Condition (ANEC) constrains the sign of one defect central charge
Summary
What information characterizes a Quantum Field Theory (QFT) uniquely? Can we use this information to classify QFTs, or map the space of QFTs? Can we prove that this information must obey constraints, eliminating regions in the space of QFTs? These questions are vitally important for many areas of physics. In contrast to the Weyl anomaly in CFTs, T μμ = 0 generically consists of contributions from both the ambient CFT, when d is even, and from defect or boundary localized terms The latter can potentially be non-vanishing for both even and odd p because a submanifold has intrinsic and extrinsic curvatures, which provides a larger basis of conformal invariants that can contribute to the anomaly. In the boundary contribution to the Weyl anomaly, they found 8 terms, including those familiar from a d = 4 CFT, namely the intrinsic Euler density and the square of the pullback of the Weyl tensor They computed all 8 central charges in one example, namely a conformally coupled free massless scalar. We use Euclidean signature throughout, with only two exceptions: our discussions of the ANEC, which requires Lorentzian signature to define null directions, and our discussions of EE, which requires a Cauchy surface to define a QFT Hilbert space
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