Global obstructions to gauge-invariance in chiral gauge theory on the lattice

Abstract

It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e. close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition $d_R^{abc}=0$ is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation.

31 pages, latex. v4: A few minor corrections, to appear in Nucl. Phys. B

References in corpus (9)

• Abelian chiral gauge theories on the lattice with exact gauge invariance
• A continuum limit of the chiral Jacobian in lattice gauge theory
• Bounds on the Wilson Dirac Operator
• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator
• Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
• Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
• Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
• Translational Anomaly in Chiral Gauge Theories on a Torus and the Overlap Formalism

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