Arbitrary parameters in implicit regularization and democracy within perturbative description of 2-dimensional gravitational anomalies

Abstract

We show that the Implicit Regularization Technique is useful to display quantum symmetry breaking in a complete regularization independent fashion. Arbitrary parameters are expressed by finite differences between integrals of the same superficial degree of divergence whose value is fixed on physical grounds (symmetry requirements or phenomenology). We study Weyl fermions on a classical gravitational background in two dimensions and show that, assuming Lorentz symmetry, the Weyl and Einstein Ward identities reduce to a set of algebraic equations for the arbitrary parameters which allows us to study the Ward identities on equal footing. We conclude in a renormalization independent way that the axial part of the Einstein Ward identity is always violated. Moreover whereas we can preserve the pure tensor part of the Einstein Ward identity at the expense of violating the Weyl Ward identities we may as well violate the former and preserve the latter.

8 pages, no figures

References in corpus (22)

• When radiative corrections are finite but undetermined
• Two-dimensional gravitational anomalies, Schwinger terms and dispersion relations
• Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework
• Techniques for one-loop calculations in constrained differential renormalization
• Consistency Relations for an Implicit n-dimensional Regularization Scheme
• Consistency in Regularizations of the Gauged NJL Model at One Loop Level
• The beta function of N=1 SYM in Differential Renormalization
• Differential Renormalization of Massive Quantum Field Theories
• Consistent Momentum Space Regularization/Renormalization of Supersymmetric Quantum Field Theories: The 3-loop beta function for the Wess-Zumino Model
• Comparing Implicit, Differential, Dimensional and BPHZ Renormalisation
• Implicit Regularization and Renormalization of QCD
• Supergravity corrections to $(g-2{)}_l$ in differential renormalization
• Algebraic Renormalization of $N=1$ Supersymmetric Gauge Theories with Supersymmetry Breaking Masses
• A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to 2-Loop Order
• Renormalization of supersymmetric Yang-Mills theories with soft supersymmetry breaking
• Differential Regularization of Chern-Simons-Maxwell Spinor and Scalar Electrodynamics
• Constrained Differential Renormalization of Yang-Mills Theories
• Renormalization Group Study of Chern-Simons Field Coupled to Scalar Matter in a Modified BPHZ Subtraction Scheme
• Gravitational and Schwinger model anomalies: how far can the analogy go?
• The Depth and Breadth of John Bell's Physics
• Gravitational anomalies in a dispersive approach
• Regularization of supersymmetric theories: Recent improvements

Cited by in corpus (23)

• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Quantum gravitational contributions to the beta function of quantum electrodynamics
• Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
• Implicit regularization beyond one loop order: gauge field theories
• Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints
• Systematization of Basic Divergent Integrals in Perturbation Theory and Renormalization Group Functions
• Supergravity corrections to the $(g-2{)}_l$ factor by Implicit Regularization
• On the equivalence between Implicit Regularization and Constrained Differential Renormalization
• The Role of hidden ambiguities in the Linear Sigma Model with fermions
• Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
• Guises and Disguises of Quadratic Divergences
• On the Bose symmetry and the left- and right-chiral anomalies
• Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach
• Implicit regularization beyond one loop order: scalar field theories
• One-loop conformal anomaly in an implicit momentum space regularization framework
• Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory
• Multiloop calculations with Implicit Regularization in massless theories
• Advances towards the systematization of calculations with Implicit Regularization
• Do anomalies break the momentum routing invariance?
• Momentum Space Regularizations and the Indeterminacy in the Schwinger Model