Nonperturbative Casimir effect and monopoles: compact Abelian gauge theory in two spatial dimensions

Abstract

We demonstrate that Casimir forces associated with zero-point fluctuations of quantum vacuum may be substantially affected by the presence of dynamical topological defects. In order to illustrate this nonperturbative effect we study the Casimir interactions between dielectric wires in a compact formulation of Abelian gauge theory in two spatial dimensions. The model possesses topological defects, instanton-like monopoles, which are known to be responsible for nonperturbative generation of a mass gap and for a linear confinement of electrically charged probes. Despite the model has no matter fields, the Casimir energy depends on the value of the gauge coupling constant. We show, both analytically and numerically, that in the strong coupling regime the Abelian monopoles make the Casimir forces short-ranged. Simultaneously, their presence increases the interaction strength between the wires at short distances for certain range of values of the gauge coupling. The wires suppress monopole density in the space between them compared to the density outside the wires. In the weak coupling regime the monopoles become dilute and the Casimir potential reduces to a known theoretical result which does not depend on the gauge coupling.

19 pages, 12 figures

References in corpus (6)

• Worldline algorithms for Casimir configurations
• Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics
• Effects of rotation and boundaries on chiral symmetry breaking of relativistic fermions
• Repulsive Casimir force between Weyl semimetals
• Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
• Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory

Cited by in corpus (19)

• Casimir effect in Yang-Mills theory
• Sign Flip in the Casimir Force for Interacting Fermion Systems
• The Casimir effect and deconfinement phase transition
• Lattice-fermionic Casimir effect and topological insulators
• Casimir Effect in (2+1)-dimensional Yang-Mills Theory as a Probe of the Magnetic Mass
• Casimir effect for lattice fermions
• Boundary states and Non-Abelian Casimir effect in lattice Yang-Mills theory
• Casimir boundaries, monopoles, and deconfinement transition in 3+1 dimensional compact electrodynamics
• Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking
• Topological defects and confinement with machine learning: the case of monopoles in compact electrodynamics
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Casimir effect in axion electrodynamics with lattice regularizations
• $D$ mesons as a probe of Casimir effect for chiral symmetry breaking
• Casimir effect with machine learning
• A black hole toy model with non-local and boundary modes from non-trivial boundary conditions
• Dual chiral density wave induced oscillating Casimir effect
• Effective model for pure Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ with Polyakov loops
• Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification
• Circumventing the black hole hair-loss problem