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

## TL;DR

This paper investigates how topological monopoles in a 2D Abelian gauge theory nonperturbatively influence Casimir forces, revealing that monopoles can make these forces short-ranged and alter interaction strengths depending on the coupling regime.

## Contribution

It provides the first detailed analysis of the nonperturbative effects of monopoles on Casimir forces in a compact Abelian gauge theory in two dimensions.

## Key findings

- Monopoles make Casimir forces short-ranged in strong coupling.
- Monopoles increase short-distance interaction strength for certain gauge couplings.
- Monopole density is suppressed between wires compared to outside.

## 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.