Induced Chern-Simons action on noncommutative torus

Abstract

We compute a Chern-Simons term induced by the fermions on noncommutative torus interacting with two U(1) gauge fields. For rational noncommutativity θ\propto P/Q we find a new mixed term in the action which involves only those fields which are (2π)/Q periodic, like the fields in a crystal with Q^2 nodes.

9 pp; v2: references and discussion added

References in corpus (16)

• Heat kernel expansion: user's manual
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Perturbative quantum gauge fields on the noncommutative torus
• Noncommutative Gauge Field Theories: A No-Go Theorem
• Gauge Invariance, Finite Temperature and Parity Anomaly in D=3
• Chern-Simons action in noncommutative space
• The spectral action for Moyal planes
• Effective QED Actions: Representations, Gauge Invariance, Anomalies and Mass Expansions
• Non-Commutative Geometry on a Discrete Periodic Lattice and Gauge Theory
• Non-commutative heat kernel
• Induced Chern-Simons and WZW action in Noncommutative Spacetime
• The $\zeta$-function answer to parity violation in three dimensional gauge theories
• Trouble with space-like noncommutative field theory
• Noncommutative Field Theory and the Dynamics of Quantum Hall Fluids
• Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
• On Double Gauging of U(1) Symmetry on Noncommutative Space

Cited by in corpus (4)

• Gravitational parity anomaly with and without boundaries
• On space-time noncommutative theories at finite temperature
• Renormalization on noncommutative torus
• A note on the topological order of noncommutative Hall fluids