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.