The Weyl anomaly in interacting quantum field theory on curved spacetimes

Abstract

We define the notion of Weyl anomalies, measuring the violation of local scale invariance, in interacting quantum field theory on curved spacetimes in the framework of locally covariant field theory. We discuss some general properties of Weyl anomalies, such as their relation to the trace anomaly. We give a criterion for a theory to be conformal at the quantum level, and show that even for a conformal theory Weyl transformations in general obtain quantum corrections. We study the trace anomaly in detail for the ${\varphi }^4$ theory, in particular determining it up to second order in the interaction. We also show that at third order in the interaction a potential $\square {\varphi }^2$ term can be removed by finite renormalization.

arXiv commentv2: Published Version

References in corpus (39)

• On Renormalization Group Flows in Four Dimensions
• The motion of point particles in curved spacetime
• Twenty Years of the Weyl Anomaly
• The generally covariant locality principle -- A new paradigm for local quantum physics
• Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
• Local Wick Polynomials and Time Ordered Products of Quantum Fields in Curved Spacetime
• Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
• Quantum fields in curved spacetime
• Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• On the Renormalization Group in Curved Spacetime
• Limit Cycles and Conformal Invariance
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Renormalized Quantum Yang-Mills Fields in Curved Spacetime
• Comments on the Stress-Energy Tensor Operator in Curved Spacetime
• Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
• Trace anomalies in chiral theories revisited
• CP-violating CFT and trace anomaly
• Removal of violations of the Master Ward Identity in perturbative QFT
• Sine-Gordon breather form factors and quantum field equations
• On the trace anomaly of a Weyl fermion
• The renormalized locally covariant Dirac field
• Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT
• Conformal generally covariant quantum field theory: The scalar field and its Wick products
• Trace Anomaly of Weyl Fermions via the Path Integral
• Superconformal quantum field theory in curved spacetime
• Trace anomaly for chiral fermions via Hadamard subtraction
• Conformal Anomaly for Non-Conformal Scalar Fields
• Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for ${\gamma }_{\ast }$
• Universal definition of the non-conformal trace anomaly
• Locally covariant charged fields and background independence
• Anomalies from an effective field theory perspective
• Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
• Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories
• Background independence in gauge theories
• The semiclassical energy density of kinks and solitons
• Chiral fermions, dimensional regularization, and the trace anomaly
• Recursive construction of the operator product expansion in curved space
• Background independence and the Adler-Bardeen theorem