$p$-form electrodynamics as edge modes of a topological field theory

TL;DR

This paper demonstrates that $p$-form electrodynamics in various dimensions can be derived as edge modes of a topological field theory, revealing new insights into their boundary dynamics and charge structures.

Contribution

It establishes a precise connection between $p$-form electrodynamics and topological field theories via Hamiltonian reduction, including cases with interactions and chiral forms.

Findings

$p$-form electrodynamics emerges as boundary modes of topological theories.

Electric and magnetic charges correspond to Noether charges in the topological framework.

Chiral $p$-forms relate to Chern-Simons theories with covariant stress-energy tensors.

Abstract

$p$-form electrodynamics in $d\geq 2$ dimensions is shown to emerge as the edge modes of a topological field theory with a precise set of boundary conditions, through the Hamiltonian reduction of its action. Electric and magnetic charges correspond to Noether ones in the topological field theory. For chiral $p$-forms, the topological action can be consistently truncated, so that the Henneaux-Teitelboim action is recovered from a pure Chern-Simons theory, with a manifestly covariant stress-energy tensor at the boundary. Topologically massive $p$-form electrodynamics as well as axion couplings are also shown to be described through this mechanism by considering suitable (self-)interaction terms in the topological theory.