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.
Highlights
Quantum mechanical symmetry breakings or anomalies are important mechanisms in the description of nature
The quantum breaking of scale and conformal invariance in quantum field theory translated by the Gell-Mann-Low renormalization group explains the diversity of particles in nature
The importance of anomalies pervades different areas in physics entering into the field of string theory [2], condensed matter and gravity and supersymmetry [4]
Summary
Quantum mechanical symmetry breakings or anomalies are important mechanisms in the description of nature. On the other hand perturbation theory may present some oddities such as preserving gauge invariance at the expense of adopting a special momentum routing [20] e.g. in the AVV triangle anomaly Amplitudes which manifest this feature usually have one axial vertex and should not be treated with naive dimensional regularization: whilst a shift in the integration variable is always possible in DR, the algebraic properties of γ5 matrix clash with analytical continuation on the spacetime dimension. In [12] we show that the quadratic divergences originated from the tadpoles are important to cancel out other quadratic divergences in QCD at one loop order in order to maintain gauge invariance
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