# Holography and $AdS_2$ gravity with a dynamical aether

## TL;DR

This paper explores two-dimensional Einstein-aether gravity with an $AdS_2$ solution, revealing full time reparametrization symmetry but also violations of conformal Ward identities, with entropy scaling logarithmically with temperature.

## Contribution

It demonstrates the full set of time reparametrizations as asymptotic symmetries and analyzes the universal horizon entropy in Einstein-aether gravity.

## Key findings

- Asymptotic symmetry group is the full time reparametrization group.
- Universal horizon entropy scales with the logarithm of temperature.
- Violation of conformal Ward identity suggests explicit symmetry breaking.

## Abstract

We study two-dimensional Einstein-aether (or equivalently Ho\v{r}ava-Lifshitz) gravity, which has an $AdS_2$ solution. We examine various properties of this solution in the context of holography. We first show that the asymptotic symmetry group is the full set of time reparametrizations, the one-dimensional conformal group. At the same time there are configurations with finite energy and temperature, which indicate a violation of the Ward identity associated with one-dimensional conformal invariance. These solutions are characterized by a universal causal horizon and we show that the associated entropy of the universal horizon scales with the logarithm of the temperature. We discuss the puzzles associated with this result and argue that the violation of the Ward identity is associated with a type of explicit breaking of time reparametrizations in the hypothetical $0+1$ dimensional dual system.