The space of transport coefficients allowed by causality

Area of Science:

• Relativistic hydrodynamics
• Theoretical physics
• Condensed matter theory

Background:

• Relativistic hydrodynamics is a fundamental theory describing fluid dynamics at relativistic speeds.
• Symmetries determine the theory up to transport coefficients, which require explicit calculation.
• Microscopic causality is a key constraint for consistent theories.

Purpose of the Study:

• To develop a general approach for constraining relativistic hydrodynamics theories.
• To identify universal properties of transport coefficients based on causality.
• To explore the geometric structure of consistent theories in the space of transport coefficients.

Main Methods:

• Employing bootstrap techniques to enforce microscopic causality.
• Analyzing the space of transport coefficients.
• Analytically constructing cross-sections of the hydrohedron.

Main Results:

• A universal convex geometry, termed the hydrohedron, is identified in the space of transport coefficients.
• All consistent relativistic hydrodynamics theories lie within or on the boundary of the hydrohedron.
• Analytical bounds on transport coefficients for sound and diffusion modes are derived for theories without stochastic fluctuations.

Conclusions:

• The hydrohedron provides a geometric framework for classifying and constraining relativistic hydrodynamics theories.
• Causality imposes significant universal constraints on the possible values of transport coefficients.
• This work establishes a new direction for studying transport coefficients using geometric and bootstrap methods.