Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
arXiv:hep-lat/0210017 · doi:10.1088/1126-6708/2003/01/075
Abstract
We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a massless theory receives an anomaly expressed by the noncommutative Chern-Simons action. The coefficient of the anomaly is labelled by an integer depending on the lattice action, which is a noncommutative counterpart of the phenomenon known in the commutative theory. The parity anomaly can also be obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed at finite lattice spacing. This suggests a natural definition of the lattice-regularized Chern-Simons theory on a noncommutative torus, which could enable nonperturbative studies of quantum Hall systems.
arXiv comment31 pages. LaTeX, feynmf. Minor changes, references added and typos corrected. Final version published in JHEP
References in corpus (59)
- Noncommutative Field Theory
- Quantum Field Theory on Noncommutative Spaces
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Noncommutative Perturbative Dynamics
- Exactly massless quarks 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
- Noncommutative Yang-Mills in IIB Matrix Model
- Magnetic fields, branes and noncommutative geometry
- Wilson Loops in Noncommutative Yang Mills
- The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
- Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
- Quantum Hall states as matrix Chern-Simons theory
- Finite N Matrix Models of Noncommutative Gauge Theory
- Nonperturbative Dynamics of Noncommutative Gauge Theory
- Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory
- Phase structure of non-commutative scalar field theories
- Open Strings in a B-field Background as Electric Dipoles
- One Loop Renormalizability of Supersymmetric Yang-Mills Theories on Noncommutative Two-Torus
- On Level Quantization for the Noncommutative Chern-Simons Theory
- Stripes from (noncommutative) stars
- Quantum Hall Physics = Noncommutative Field Theory
- Gauge Invariance, Finite Temperature and Parity Anomaly in D=3
- A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
- Chern-Simons action in noncommutative space
- Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
- Overlap in odd dimensions
- Chern-Simons Theories on Noncommutative Plane
- Non-Commutative Geometry on a Discrete Periodic Lattice and Gauge Theory
- Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
- Absence of Higher Order Corrections to Noncommutative Chern-Simons Coupling
- Noncommutative Chiral Gauge Theories on the Lattice with Manifest Star-Gauge Invariance
- Proposal for the numerical solution of planar QCD
- A Note on Noncommutative Chern-Simons Theories
- Simulating non-commutative field theory
- Non-commutative Chern-Simons for the Quantum Hall System and Duality
- Wess-Zumino-Witten and fermion models in noncommutative space
- Induced Chern-Simons and WZW action in Noncommutative Spacetime
- One-loop Shift in Noncommutative Chern-Simons Coupling
- Thermal effects in perturbative noncommutative gauge theories
- Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
- Chiral Anomaly on Fuzzy 2-Sphere
- Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories
- Noncommutative Chern-Simons terms and the noncommutative vacuum
- The Wess-Zumino-Witten term in non-commutative two-dimensional fermion models
- Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids
- *-Wars Episode I: The Phantom Anomaly
- Chiral anomalies in noncommutative gauge theories
- The Chern-Simons Action in Non-Commutative Geometry
- Non-commutative principal chiral models
- Ginsparg-Wilson Fermions in Odd Dimensions
- Chiral anomalies in the reduced model
- Parity Invariant Lattice Regularization of Three-Dimensional Gauge-Fermion System
- Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope
- The covariant form of the gauge anomaly on noncommutative R2n
- Discrete Noncommutative Gauge Theory
- Matrix model and noncommutative Chern-Simons theory
- Reduced Models and Noncommutative Gauge Theories
Cited by in corpus (12)
- Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
- Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere
- The Fuzzy Disc
- Dynamical generation of a nontrivial index on the fuzzy 2-sphere
- Supersymetry on the Noncommutative Lattice
- Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
- Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus
- Admissibility Condition and Nontrivial Indices on a Noncommutative Torus
- The U(1)A anomaly in noncommutative SU(N) theories
- Towards Noncommutative Fuzzy QED
- Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
- Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons