  We present a new Higgsless model of superconductivity, inspired from anyon
superconductivity but P- and T-invariant and generalizable to any dimension.
While the original anyon superconductivity mechanism was based on
incompressible quantum Hall fluids as average field states, our mechanism
involves topological insulators as average field states. In D space dimensions
it involves a (D-1)-form fictitious pseudovector gauge field which originates
from the condensation of topological defects in compact low-energy effective BF
theories. In the average field approximation, the corresponding uniform
emergent charge creates a gap for the (D-2)-dimensional branes via the Magnus
force, the dual of the Lorentz force. One particular combination of intrinsic
and emergent charge fluctuations that leaves the total charge distribution
invariant constitutes an isolated gapless mode leading to superfluidity. The
remaining massive modes organise themselves into a D-dimensional charged,
massive vector. There is no massive Higgs scalar as there is no local order
parameter. When electromagnetism is switched on, the photon acquires mass by
the topological BF mechanism. Although the charge of the gapless mode (2) and
the topological order (4) are the same as those of the standard Higgs model,
the two models of superconductivity are clearly different since the origins of
the gap, reflected in the high-energy sectors are totally different. In 2D this
type of superconductivity is explicitly realized as global superconductivity in
Josephson junction arrays. In 3D this model predicts a possible phase
transition from topological insulators to Higgsless superconductors.
