The Non-Abelian Casimir Effect for Plates, Symmetrical Tube and Box on the Lattice

TL;DR

This paper presents non-perturbative calculations of the Casimir effect in non-abelian SU(3) gauge theory, exploring complex geometries like tubes and boxes, and finds that the Casimir force remains attractive across phases and geometries.

Contribution

First non-perturbative analysis of Casimir effects in non-abelian gauge theories for complex geometries beyond parallel plates.

Findings

Casimir effect is attractive for symmetrical tube and box geometries.

The Casimir potential differs from scalar field theory predictions.

Temperature change does not affect the Casimir potential.

Abstract

We present non-perturbative results of the Casimir potential in non-abelian SU(3) gauge theory in (2+1)D and (3+1)D in the confined and deconfined phase. For the first time, geometries beyond parallel plates in (3+1)D are explored and we show that the Casimir effect for the symmetrical tube and symmetrical box is attractive. The Casimir potential for the tube differs from the massless non-interacting scalar field theory prediction, where a repulsive Casimir potential is expected. Unlike the parallel plate geometry where the plate-size is fixed, in the case of the tube and box, the sizes of the faces forming the walls of the geometries changes with separation distance. We propose various methods that can be used to account for the energy contributions from creating the boundaries. We show that increasing the temperature from a confined to a deconfined phase does not alter the Casimir potential. This observation is consistent with prior work suggesting that the region inside the walls is a boundary induced deconfined phase.