Chiral lattice fermions, minimal doubling, and the axial anomaly

Journal Article · Sun Aug 01 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.034511· OSTI ID:21432887

Tiburzi, B C ^[1]

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1. Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States)

Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity, we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from nonconservation of the flavor-singlet current. Similar nonconservation also leads to the axial anomaly in the case of the naieve lattice action. For minimally doubled actions, however, fine-tuning of the action and axial current is necessary to arrive at the anomaly. Conservation of the flavor nonsinglet vector current additionally requires the current to be fine-tuned. Finally, we determine that the chiral projection of a minimally doubled fermion action can be used to arrive at a lattice theory with an undoubled Dirac fermion possessing the correct anomaly in the continuum limit.

• OSTI ID: 21432887
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 3 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRAIC CURRENTS
AXIAL SYMMETRY
CHIRAL SYMMETRY
CHIRALITY
COMPOSITE MODELS
CONSTRUCTIVE FIELD THEORY
CURRENTS
FERMIONS
FIELD THEORIES
FLAVOR MODEL
INTERACTIONS
LATTICE FIELD THEORY
MATHEMATICAL MODELS
PARTICLE MODELS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
QUARK MODEL
SYMMETRY
VECTOR CURRENTS