# Emergent Higgsless Superconductivity

## TL;DR

This paper introduces a novel Higgsless superconductivity model based on topological insulators and BF theories, differing fundamentally from traditional Higgs-based mechanisms and applicable across multiple dimensions.

## Contribution

The paper proposes a new topological, Higgsless superconductivity mechanism involving BF theories and topological defects, generalizable to any dimension and distinct from conventional models.

## Key findings

- Photon acquires mass via topological BF mechanism.
- In 2D, realized as global superconductivity in Josephson junction arrays.
- Predicts a phase transition from topological insulators to Higgsless superconductors in 3D.

## Abstract

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. 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.