Casimir effect in Yang-Mills theories

TL;DR

This paper investigates the Casimir effect in Yang-Mills theories with a boundary, demonstrating that a mass gap suppresses the effect exponentially, aligning with lattice computations.

Contribution

It provides a novel analytical approach using Dyson-Schwinger equations to study the Casimir effect in Yang-Mills theories with a boundary.

Findings

Mass gap causes exponential suppression of the Casimir effect.

Results align well with recent lattice computations.

Analytical method via Dyson-Schwinger equations applied to boundary effects.

Abstract

We study both massless scalar and Yang-Mills field theories in the deep infrared in presence of a simple boundary. We can show, with the help of the recent scenario emerging from studies on the propagators, that the presence of a mass gap makes the Casimir contribution exponentially small as should be expected. We obtain our result from the solution of the Dyson-Schwinger set of equations obtained in form of partial differential equations. Our results agree fairly well with recent lattice computations.