Axial anomaly in the reduced model: Higher representations
arXiv:hep-lat/0305011 · doi:10.1088/1126-6708/2003/05/042
Abstract
The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$\U(1)$ embedding'' with ). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large limit. The large limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is $\SU(N)$, it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.
21 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHEP
References in corpus (49)
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Exactly massless quarks on the lattice
- A Large-N Reduced Model as Superstring
- Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
- 4d Conformal Field Theories and Strings on Orbifolds
- 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
- Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
- Abelian chiral gauge theories on the lattice with exact gauge invariance
- Finite N Matrix Models of Noncommutative Gauge Theory
- Prospects for perfect actions
- Nonperturbative Dynamics of Noncommutative Gauge Theory
- IIB Matrix Model
- A continuum limit of the chiral Jacobian in lattice gauge theory
- Topology and the axial anomaly in abelian lattice gauge theories
- Bounds on the Wilson Dirac Operator
- Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly
- Duality of Non-Supersymmetric Large N Gauge Theories
- Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator
- Chiral Fermions on the Lattice
- On the overlap formulation of chiral gauge theory
- Axial anomaly and topological charge in lattice gauge theory with Overlap Dirac operator
- Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
- Lattice regularization of chiral gauge theories to all orders of perturbation theory
- Consistent and covriant anomalies in the overlap formulation of chiral gauge theories
- Proposal for the numerical solution of planar QCD
- Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance
- On the Overlap Prescription for Lattice Regularization of Chiral Fermions
- Anomaly Cancellation Condition in Lattice Gauge Theory
- On the continuum limit of fermionic topological charge in lattice gauge theory
- Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice
- Overlap formulation of Majorana--Weyl fermions
- Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
- Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
- Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
- Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
- The axial anomaly in lattice QED. A universal point of view
- Fermions on tori in uniform abelian fields
- Unitary IIB Matrix Model and the Dynamical Generation of the Space Time
- Chiral anomalies in the reduced model
- Universality of the Axial Anomaly in Lattice QCD
- More about the axial anomaly on the lattice
- On the supersymmetric formulation of Unitary Matrix Model of type IIB