Chern-Simons foam

TL;DR

This paper extends Chern-Simons theory to non-manifold cell complexes, deriving gauge-invariant actions, interaction terms, and conservation laws at intersections, broadening its applicability to complex network-like structures.

Contribution

It introduces a framework for defining gauge-invariant Chern-Simons actions on cell complexes, including interaction terms and charge conservation laws at intersections.

Findings

Gauge invariance determines the action and interaction terms.

Relations between coupling constants at intersections are established.

Conservation laws for charges at intersections are derived.

Abstract

Chern-Simons theory can be defined on a cell complex, such as a network of bubbles, which is not a (Hausdorff) manifold. Requiring gauge invariance determines the action, including interaction terms at the intersections, and imposes a relation between the coupling constants of the CS terms on adjacent cell walls. We also find simple conservation laws for charges at the intersections.