Higgs effect without lunch

Reduction in effective space–time dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wave function factors depend non-trivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a ‘covert’ pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. The Stueckelberg mode remains in the theory as a propagating scalar degree of freedom from a dimensionally reduced perspective, but it is not ‘eaten’ in a mass-generating mechanism. At leading order, it also makes no contribution to the conserved energy; for this reason, it may be called a (non-ghost) ‘phantom’. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.