# Generalizations of the Pontryagin and Husain-Kucha\v{r} actions to manifolds with boundary

## TL;DR

This paper explores generalized actions related to Pontryagin and Husain-Kuchař theories on manifolds with boundaries, revealing connections to known models like 3D Euclidean gravity and analyzing their physical content via Hamiltonian methods.

## Contribution

It introduces new generalizations of classical actions on manifolds with boundary and applies Hamiltonian analysis to clarify their physical and dynamical structures.

## Key findings

- Connections to 3D Euclidean gravity with cosmological constant
- Identification of boundary and bulk models within the generalizations
- Application of geometric Dirac algorithm to boundary-including systems

## Abstract

In this paper we study a family of generalizations of the Pontryagin and Husain-Kucha\v{r} actions on manifolds with boundary. In some cases, they describe well-known models---either at the boundary or in the bulk---such as 3-dimensional Euclidean general relativity with a cosmological constant or the Husain-Kucha\v{r} model. We will use Hamiltonian methods in order to disentangle the physical and dynamical content of the systems that we discuss here. This will be done by relying on a geometric implementation of the Dirac algorithm in the presence of boundaries recently proposed by the authors.