Anomalies, Local Counter Terms and Bosonization

Abstract

We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spurious and eliminated by a local counter term corresponding to the mass term of the gauge field in gauge theory, cannot be removed by a {\it local} counter term and plays a central role by giving the kinetic term of the bosonized field in the context of path integral bosonization.

24 pages, A contribution to the Hidenaga Yamagishi commemorative volume of Physics Reports, edited by E. Witten and I. Zahed. Some sentences were made more precise, and a Note Added was added

Cited by in corpus (11)

• A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
• From Luttinger liquid to Altshuler-Aronov anomaly in multi-channel quantum wires
• Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly
• Bosonization with a background $U(1)$ gauge field
• Temporal Chiral Spiral in Strong Magnetic Fields
• Quantum anomalies and some recent developments
• Anomalous gauge theories revisited
• Sigma model on a squashed sphere with a Wess-Zumino term
• A non covariant fermionic determinant and its connection to Luttinger systems
• Near-SUSY to Non-SUSY Crossover
• Bosonization in the path integral formulation