# Universal low temperature theory of charged black holes with AdS$_2$ horizons

## TL;DR

This paper derives a universal low-temperature effective quantum theory for charged AdS black holes with AdS$_2$ horizons, capturing their near-horizon physics and thermodynamics in a 0+1 dimensional framework.

## Contribution

It provides a derivation of the universal effective theory from the full Einstein-Maxwell theory, including quantitative couplings consistent with black hole thermodynamics.

## Key findings

- Effective theory is a Schwarzian action with a phase mode.
- Couplings match thermodynamic expectations.
- Universal description applies to a class of charged AdS black holes.

## Abstract

We consider the low temperature quantum theory of a charged black hole of zero temperature horizon radius $R_h$, in a spacetime which is asymptotically AdS$_{D}$ ($D > 3$) far from the horizon. At temperatures $T \ll 1/R_h$, the near-horizon geometry is AdS$_2$, and the black hole is described by a universal 0+1 dimensional effective quantum theory of time diffeomorphisms with a Schwarzian action, and a phase mode conjugate to the U(1) charge. We obtain this universal 0+1 dimensional effective theory starting from the full $D$-dimensional Einstein-Maxwell theory, while keeping quantitative track of the couplings. The couplings of the effective theory are found to be in agreement with those expected from the thermodynamics of the $D$-dimensional black hole.