Boundary conformal invariants and the conformal anomaly in five dimensions

Abstract

In odd dimensions the integrated conformal anomaly is entirely due to the boundary terms \cite{Solodukhin:2015eca}. In this paper we present a detailed analysis of the anomaly in five dimensions. We give the complete list of the boundary conformal invariants that exist in five dimensions. Additionally to 8 invariants known before we find a new conformal invariant that contains the derivatives of the extrinsic curvature along the boundary. Then, for a conformal scalar field satisfying either the Dirichlet or the conformal invariant Robin boundary conditions we use the available general results for the heat kernel coefficient $a_5$, compute the conformal anomaly and identify the corresponding values of all boundary conformal charges.

18 pages, no figures; typo in eq.(33) corrected

References in corpus (22)

• Heat kernel expansion: user's manual
• Twenty Years of the Weyl Anomaly
• A Constraint on Defect and Boundary Renormalization Group Flows
• Boundary Conformal Field Theory and a Boundary Central Charge
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• Displacement Operators and Constraints on Boundary Central Charges
• Boundary terms of conformal anomaly
• Heat kernel asymptotics with mixed boundary conditions
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
• Corner contributions to holographic entanglement entropy in AdS4/BCFT3
• Anomalies, entropy and boundaries
• Conformal anomalies of CFT's with boundaries
• The $a_5$ heat kernel coefficient on a manifold with boundary
• Defect $a$-Theorem and $a$-Maximization
• Boundary effects in entanglement entropy
• Holographic calculation of entanglement entropy in the presence of boundaries
• The asymptotics of the Laplacian on a manifold with boundary II
• Boundary-corner entanglement for free bosons
• Conformally invariant wave equation for a symmetric second rank tensor ("spin-2") in d-dimensional curved background
• Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls
• Singular Yamabe Problem Willmore Energies
• Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models

Cited by in corpus (8)

• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Curvature Invariants for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime
• Interacting conformal scalar in a wedge
• Boundaries in Free Higher Derivative Conformal Field Theories
• Method of images in defect conformal field theories
• Defect Localized Entropy: Renormalization Group and Holography
• Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory