On the introduction of a boundary in topological field theories

TL;DR

This paper explores how boundaries affect topological field theories across dimensions, characterizing boundary actions and revealing their covariance, with applications to models like the 2D Luttinger liquid and 4D Maxwell theory.

Contribution

It provides a general characterization of boundary actions in topological field theories and connects physical models to boundary reductions of higher-dimensional theories.

Findings

Boundary actions are uniquely characterized and covariant.

Physical models can be derived as boundary reductions of higher-dimensional theories.

Topological theories lack local observables but have meaningful boundary dynamics.

Abstract

We study the consequences of the presence of a boundary in topological field theories in various dimensions. We characterize, univocally and on very general grounds, the field content and the symmetries of the actions which live on the boundary. We then show that these actions are covariant, despite appearances. We show also that physically relevant theories like the 2D Luttinger liquid model, or the 4D Maxwell theory, can be seen as boundary reductions of higher dimensional topological field theories, which do not display local observables.