Perturbation calculation of the axial anomaly of Ginsparg-Wilson fermion

1999/01/17 by Ting-Wai Chiu, Tung-Han Hsieh, Chiu, Ting-Wai +2 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-lat #hep-ph #hep-th

paper · pdf · doi:10.48550/arxiv.hep-lat/9901011

38 pages, latex, 1 figure, add appendix C and several remarks

openalex publication_date 1999/01/17 · arxiv created 1999/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We evaluate the axial anomaly for the general Ginsparg-Wilson fermion operator D = D_c (\Id + R D_c)^-1 with R = r \Id. For any chirally symmetric D_c which in the free fermion limit, is free of species doubling and behaves like i γ_μp_μ as p → 0, the axial anomaly \tr[γ₅ (R D) (x,x)] for U(1) lattice gauge theory with single fermion flavor is equal to e²/(32 π²) ε_μνλσ F_μν(x) F_λσ(x+μ+ν) plus terms which are higher orders and/or non-perturbative contribtuons. The F F term is r-invariant and has the correct continuum limit.

Cited by

• A lattice implementation of the eta-invariant and effective action for chiral fermions on the lattice

Related

• Lattice Fermions and the Chiral Anomaly
• Fermion decoupling and the axial anomaly on the lattice
• Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice
• Generalized Ginsparg-Wilson relations
• Chiral Anomalies In Field Theories