Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip

Abstract

We study how boundaries affect Maxwell-Chern-Simons theory, a three-dimensional gauge theory that combines ordinary electromagnetic propagation with a topological Chern-Simons term. On a strip, the two boundaries can support edge excitations while the single massive bulk mode mediates a Casimir interaction between them. We use Symanzik's local boundary-field-theory framework, deriving the boundary conditions from the most general quadratic local boundary action considered here rather than imposing them by hand. Requiring these conditions to act consistently on the unique physical bulk mode selects a continuous family of admissible boundaries, characterized by an impedance and an edge velocity. The associated conserved currents form two boundary current algebras with opposite levels, and for a symmetric strip the edge modes propagate in opposite directions. The bulk and residual edge sectors factorize, leaving a single physical scattering channel for the Casimir problem. We derive its reflection amplitude, identify a stable pole-free domain, and show that the force is attractive there. In the Maxwell limit the usual long-range one-channel Casimir interaction is recovered, whereas the topological mass produces exponential screening at large separation. Outside the pole-free domain, localized surface modes can appear and must be included separately. The analysis provides a unified description of edge dynamics, boundary conditions and vacuum forces in a topologically massive gauge theory.

41 pages, 2 figures

References in corpus (27)

• New Developments in the Casimir Effect
• Topological orders and Edge excitations in FQH states
• Heat kernel expansion: user's manual
• Casimir forces between arbitrary compact objects
• Scattering Theory Approach to Electrodynamic Casimir Forces
• Opposites Attract - A Theorem About The Casimir Force
• Self-adjoint extensions of operators and the teaching of quantum mechanics
• The Casimir effect within scattering theory
• Global Theory of Quantum Boundary Conditions and Topology Change
• Casimir force for a sphere in front of a plane beyond Proximity Force Approximation
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• Maxwell-Chern-Simons Theory With Boundary
• On the introduction of a boundary in topological field theories
• Covariant fracton gauge theory with boundary
• 3+1D Massless Weyl spinors from bosonic scalar-tensor duality
• From Chern-Simons to Tomonaga-Luttinger
• Holographic reduction of Maxwell-Chern-Simons theory
• Holographic Projection of Electromagnetic Maxwell Theory
• Conserved chiral currents on the boundary of 3D Maxwell theory
• Topological BF description of 2D accelerated chiral edge modes
• The Scattering Approach to the Casimir Force
• Topologically protected duality on the boundary of Maxwell-BF theory
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Quasi-topological fractons: a 3D dipolar gauge theory
• Quasi-topological mass generation for 3D linearized gravity
• Covariant field theory of 3D massive fractons
• Edge modes in Chern-Simons theory on a strip