# Quintessential Quartic Quasi-topological Quartet

## TL;DR

This paper develops a new class of higher curvature gravity theories extending quasi-topological gravity to quartic order, with unique properties and applications to black hole solutions and holography.

## Contribution

It introduces the quartic generalized quasi-topological gravity, including four new nontrivial terms in four dimensions, and explores their implications for black holes and holographic duals.

## Key findings

- Constructed four-dimensional black hole solutions.
- Found that solutions deviate from universal properties in higher dimensions.
- Theories propagate only massless gravitons on symmetric backgrounds.

## Abstract

We construct the quartic version of generalized quasi-topological gravity, which was recently constructed to cubic order in arXiv: 1703.01631. This class of theories includes Lovelock gravity and a known form of quartic quasi-topological gravity as special cases and possess a number of remarkable properties: (i) In vacuum, or in the presence of suitable matter, there is a single independent field equation which is a total derivative. (ii) At the linearized level, the equations of motion on a maximally symmetric background are second order, coinciding with the linearized Einstein equations up to a redefinition of Newton's constant. Therefore, these theories propagate only the massless, transverse graviton on a maximally symmetric background. (iii) While the Lovelock and quasi-topological terms are trivial in four dimensions, there exist four new generalized quasi-topological terms (the quartet) that are nontrivial, leading to interesting higher curvature theories in $d \geq 4$ dimensions that appear well suited for holographic study. We construct four dimensional black hole solutions to the theory and study their properties. A study of black brane solutions in arbitrary dimensions reveals that these solutions are modified from the `universal' properties these solutions have. This result may lead to interesting consequences for the dual CFTs.