Anomalous gauge theories revisited
arXiv:hep-lat/0412041 · doi:10.1088/1126-6708/2005/01/051
Abstract
A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, {\it all} anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact $\U(1)$ link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear.
1+17 pages, uses JHEP3.cls, the final version to appear in JHEP, a note added
References in corpus (45)
- Exactly massless quarks on the lattice
- A Method for Simulating Chiral Fermions on the Lattice
- Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
- A construction of lattice chiral gauge theories
- More about exactly massless quarks on the lattice
- The index theorem in QCD with a finite cut-off
- Locality properties of Neuberger's lattice Dirac operator
- Chiral Determinant as an Overlap of Two Vacua
- Infinitely many regulator fields for chiral fermions
- Chiral Fermions on the Lattice
- Lattice QCD without tuning, mixing and current renormalization
- Abelian chiral gauge theories on the lattice with exact gauge invariance
- Exact chiral symmetry, topological charge and related topics
- Prospects for perfect actions
- Topology and the axial anomaly in abelian lattice gauge theories
- Bounds on the Wilson Dirac Operator
- Weyl fermions on the lattice and the non-abelian gauge anomaly
- Chiral Fermions on the Lattice
- Overlap in odd dimensions
- On the overlap formulation of chiral gauge theory
- Geometrical aspects of chiral anomalies in the overlap
- Ginsparg-Wilson relation and the overlap formula
- Lattice regularization of chiral gauge theories to all orders of perturbation theory
- Lattice Chiral Gauge Theories
- Consistent and covriant anomalies in the overlap formulation of chiral gauge theories
- On the Overlap Prescription for Lattice Regularization of Chiral Fermions
- Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
- Anomaly Cancellation Condition in Lattice Gauge Theory
- Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak 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
- Noncompact chiral U(1) gauge theories on the lattice
- Global Anomalies in chiral gauge theories on the lattice
- Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
- Global obstructions to gauge-invariance in chiral gauge theory on the lattice
- Index of a family of lattice Dirac operators and its relation to the non-abelian anomaly on the lattice
- Gauge fixing, families index theory, and topological features of the space of lattice gauge fields
- On Witten's global anomaly for higher SU(2) representations
- Anomalies, Local Counter Terms and Bosonization
- Chiral anomalies in the reduced model
- Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
- Errata and Addenda to ``Anomaly Cancellation Condition in Lattice Gauge Theory''
- More about the axial anomaly on the lattice
- Families index theory for Overlap lattice Dirac operator. I
- Wess-Zumino-Witten term on the lattice