# Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking

## TL;DR

This paper reviews nonperturbative Casimir effects in quantum field theories that model phenomena like confinement and chiral symmetry breaking, highlighting their implications in theories similar to QCD.

## Contribution

It provides a comprehensive overview of Casimir effects in nonperturbative field-theoretical models such as sigma models and gauge theories, connecting vacuum fluctuations to QCD-like phenomena.

## Key findings

- Casimir energy influences phase transitions in nonperturbative models
- Vacuum fluctuations are affected by boundary conditions in these theories
- Insights into confinement and chiral symmetry breaking mechanisms

## Abstract

The Casimir effect is a quantum phenomenon rooted in the fact that vacuum fluctuations of quantum fields are affected by the presence of physical objects and boundaries. Since the energy spectrum of the vacuum fluctuations depends on distances between (and geometries of) physical bodies, the quantum vacuum exerts a small but experimentally detectable force on neutral objects. Usually, the associated Casimir energy is calculated for free or weakly coupled quantum fields. We review recent studies of the Casimir effect in field-theoretical models which mimic features of non-perturbative QCD such as chiral or deconfining phase transitions. We discuss ${{\mathbb C}P}^{\,N-1}$ sigma model and chiral Gross-Neveu model in (1+1) dimensions as well as compact U(1) gauge theory and Yang-Mills theory in (2+1) dimensions.