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