# A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity

## TL;DR

This paper introduces a straightforward derivation of the boundary term in Lanczos-Lovelock gravity, clarifying boundary contributions and degrees of freedom, with a specific focus on the Gauss-Bonnet case.

## Contribution

It provides a new, direct derivation method for the boundary term in Lanczos-Lovelock gravity from the action principle itself.

## Key findings

- Derived the boundary term directly from the action principle.
- Clarified the boundary degrees of freedom and conjugate momenta.
- Provided a specific derivation for the Gauss-Bonnet case.

## Abstract

We present a novel derivation of the boundary term for the action in Lanczos-Lovelock gravity, starting from the boundary contribution in the variation of the Lanczos-Lovelock action. The derivation presented here is straightforward, i.e., one starts from the Lanczos-Lovelock action principle and the action itself dictates the boundary structure and hence the boundary term one needs to add to the action to make it well-posed. It also gives the full structure of the contribution at the boundary of the complete action, enabling us to read off the degrees of freedom to be fixed at the boundary, their corresponding conjugate momenta and the total derivative contribution on the boundary. We also provide a separate derivation of the Gauss-Bonnet case.