The Hydrohedron: Bootstrapping Relativistic Hydrodynamics

TL;DR

This paper introduces the hydrohedron, a universal convex geometry constraining relativistic hydrodynamics transport coefficients by enforcing microscopic causality, providing a new bootstrap-based approach to understanding hydrodynamic theories.

Contribution

It applies bootstrap techniques to relativistic hydrodynamics, defining the hydrohedron as a geometric constraint on transport coefficients based on causality.

Findings

Defined the hydrohedron as a convex geometry of consistent transport coefficients.

Constructed analytical bounds on sound and diffusion mode coefficients.

Provided a new perspective on the landscape of hydrodynamic theories.

Abstract

As an effective theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. A lot of effort has been devoted to explicit calculations of these coefficients. Here we propose a shift in perspective: we deploy bootstrap techniques to rule out theories that are inconsistent with microscopic causality. What remains is a universal convex geometry in the space of transport coefficients, which we call the hydrohedron. The landscape of all consistent theories necessarily lie inside or on the edges of the hydrohedron. We analytically construct cross-sections of the hydrohedron corresponding to bounds on transport coefficients that appear in sound and diffusion modes for theories without stochastic fluctuations.