Casimir scaling in gauge theories with a gap. Deformed QCD as a toy model

TL;DR

This paper demonstrates that a deformed version of QCD exhibits Casimir-like energy scaling with system size, due to non-dispersive contact terms, challenging traditional expectations based on massive propagating degrees of freedom.

Contribution

It reveals that in deformed QCD, Casimir-like effects arise from contact terms, not propagating particles, leading to L^{-1} energy scaling despite a mass gap.

Findings

Energy difference scales as L^{-1} in deformed QCD.

Casimir-like behavior originates from contact terms, not physical particles.

Implications for cosmology if similar effects occur in real QCD.

Abstract

We study a Casimir-like behaviour in a "deformed QCD". We demonstrate that for the system defined on a manifold of size L the difference Delta E between the energies of a system in a non-trivial background and Minkowski space-time geometry exhibits the Casimir-like scaling Delta E \sim L^{-1}, despite the presence of a mass gap in the system, in contrast with naive expectation Delta E \sim \exp(-m L), which would normally originate from any physical massive propagating degrees of freedom consequent to conventional dispersion relations. The Casimir-like behaviour in our system comes instead from a non-dispersive ("contact") term which is not related to any physical propagating degrees of freedom, such that the naive argument is simply not applicable. These ideas can be explicitly tested in weakly coupled deformed QCD. We comment on profound consequences for cosmology of this effect if it persists in real strongly coupled QCD.