Higher condensation theory

Understand

We develop a unified mathematical theory of defect condensations for topological orders in all dimensions based on higher categories, higher algebras and higher representations.

• A k-codimensional topological defect $A$ in an n+1D (potentially anomalous) topological order $C^{n+1}$ is condensable if it is equipped with the structure of a condensable $E_k$-algebra.
• Condensing such a defect $A$ amounts to a k-step process.
• In the first step, we condense the defect $A$ along one of its transversal directions, thus obtaining a (k-1)-codimensional defect $\Sigma A$, which is naturally equipped with the structure of a condensable $E_{k-1}$-algebra.