# Viscosity, Black Holes, and Quantum Field Theory

## TL;DR

This paper reviews how the AdS/CFT correspondence helps understand finite-temperature field theory, focusing on hydrodynamics, black hole duals, and the universal viscosity/entropy ratio, with implications for real physical systems.

## Contribution

It demonstrates the connection between hydrodynamic behavior and black hole quasinormal modes, and proves the universality of the viscosity/entropy ratio in theories with gravity duals.

## Key findings

- Hydrodynamic modes correspond to black hole quasinormal modes.
- The viscosity/entropy ratio is universal across a class of theories.
- A viscosity bound conjecture is formulated.

## Abstract

We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasinormal modes of the AdS black p-brane metric. We provide a proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned.