# Holographic relationships in Lovelock type brane gravity

## TL;DR

This paper demonstrates that Lovelock type brane gravity inherently exhibits holographic properties, establishing a direct correspondence between bulk and surface terms in the action, and relating conserved tensors and geometric degrees of freedom.

## Contribution

It establishes a natural holographic relationship in Lovelock brane gravity, linking bulk and surface terms and conserved tensors, which was not previously demonstrated.

## Key findings

- Bulk and surface Lagrangian terms are fully related.
- Conserved tensors in the theory are interconnected.
- Geometric degrees of freedom correspondence is discussed.

## Abstract

We show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the $\mathcal{L}_{\mbox{\tiny bulk}}$ and $\mathcal{L}_{\mbox{\tiny surf}}$ allowing $\mathcal{L}_{\mbox{\tiny surf}}$ to be determined completely by $\mathcal{L}_{\mbox{\tiny bulk}}$. In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geometric degrees of freedom in both bulk and surface space.