Anomaly Cancellation Condition in Lattice Gauge Theory

Abstract

We study the gauge anomaly $\mathcal{A}$ defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) $\mathcal{A}$ depends smoothly and locally on the gauge potential, (II) $\mathcal{A}$ reproduces the gauge anomaly in the continuum theory in the classical continuum limit, and (III) U(1) gauge anomalies have a topological property. It is then shown that the gauge anomaly $\mathcal{A}$ can always be removed by local counterterms to all orders in powers of the gauge potential, leaving possible breakings proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak $\Vert U(n,\mu )-1\Vert <{\epsilon }^{\prime }$, where $U(n,\mu )$ is the link variable and ${\epsilon }^{\prime }$ a certain small positive constant.

uses phyzzx.tex and phyzzx.plus, 57 pages, the final version to appear in Nucl. Phys. B

References in corpus (4)

• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
• Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
• Global anomalies in Chiral Lattice Gauge Theory

Cited by in corpus (34)

• Local BRST cohomology in gauge theories
• Lattice Chiral Gauge Theories
• SU(N) chiral gauge theories on the lattice
• Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice
• Real Representation in Chiral Gauge Theories on the Lattice
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Lattice 2001: Reflections
• CP breaking in lattice chiral gauge theories
• Locality Properties of a New Class of Lattice Dirac Operators
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Gauge fixing, families index theory, and topological features of the space of lattice gauge fields
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Differential Geometry of Group Lattices
• Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
• Chiral anomalies in the reduced model
• Towards Weyl fermions on the lattice without artefacts
• More about the axial anomaly on the lattice
• A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance
• Fermion-number violation in regularizations that preserve fermion-number symmetry
• Domain wall fermion and CP symmetry breaking
• New overlap construction of Weyl fermions
• A construction of the Glashow-Weinberg-Salam model on the lattice with exact gauge invariance
• Majorana and Majorana-Weyl fermions in lattice gauge theory
• Six-dimensional regularization of chiral gauge theories
• Vortex fermion on the lattice
• A numerical solution to the local cohomology problem in U(1) chiral gauge theories
• Anomalous gauge theories revisited
• Lattice QCD with fixed topology
• Axial anomaly in the reduced model: Higher representations
• Wess-Zumino-Witten term on the lattice
• CP breaking in lattice chiral gauge theory
• Another approach to local cohomology problem in abelian lattice gauge theories
• Chiral symmetry on the lattice
• CP symmetry and lattice chiral gauge theories