Hot Gauge Theory and Plasma EFTs

A weakly coupled hot non-Abelian plasma contains several parametrically different momentum and time scales. Matching between effective theories connects hard particles, screened electric fields, ultrasoft magnetic fields, and transport.

Enter this chapter

Begin with Scale Hierarchies in Hot Gauge Theories to separate the hard, electric, and magnetic scales of a hot gauge plasma.

Helpful background. Scale Hierarchies in Hot Gauge Theories and QCD Fields, Scales, and the Perturbative Domain develop the definitions used by the chapter’s opening pages.

Topics

1. Scale Hierarchies in Hot Gauge Theories — Which hard, soft-electric, ultrasoft-magnetic, frequency, formation-time, and occupancy scales organize a weakly coupled hot gauge plasma?
2. EQCD, MQCD, and Dimensional Reduction — How are EQCD and MQCD matched from hot non-Abelian gauge theory, and which static observables and nonperturbative inputs does each theory control?
3. Hard-Thermal-Loop Effective Theory — How do hard thermal particles induce gauge-invariant nonlocal HTL self-energies and vertices for soft gauge fields?
4. Collective Modes and Dynamical Screening — What do longitudinal and transverse collective modes, Landau damping, static screening, and infrared spectral weight look like in a hot gauge plasma?
5. The Magnetostatic Sector and Linde Problem — Why does the g²T magnetostatic sector remain nonperturbative and impose the Linde obstruction on high-order thermal gauge observables?
6. Ultrasoft Color Dynamics and Bödeker Theory — How does matching HTL dynamics through a color Boltzmann conductivity produce Bödeker’s overdamped ultrasoft Langevin theory and its topological-diffusion rate?
7. Gauge-Theory Effective Kinetic Theory — How does leading-order gauge-theory effective kinetic theory combine screened elastic scattering, collinear splitting, inverse processes, and LPM interference without double counting?
8. Weak-Coupling Plasma Transport Coefficients — How are weak-coupling shear viscosity, diffusion, conductivity, momentum broadening, and related plasma transport coefficients extracted from EKT or correlators?
9. Non-Abelian Plasma Instabilities — How do anisotropic distributions produce non-Abelian plasma instabilities, what controls their nonlinear saturation, and what evidence separates their contribution to isotropization from thermalization?

How the ideas fit together

When the gauge coupling is small, hard momenta of order the temperature can be integrated out to describe softer fields. Static dimensional reduction and real-time hard-thermal-loop response retain different information: a screening calculation does not automatically determine damping or transport. Collision-driven transport further requires screened scattering and coherent collinear processes Arnold, Moore, and Yaffe 2003, §§ 2–3.

At the magnetic scale the retained static non-Abelian theory becomes strongly coupled. Making the hard coupling small separates this sector; it does not make its infrared dynamics perturbative. Anisotropic distributions introduce another limitation because unstable modes can invalidate an equilibrium expansion.

Where to go next

Continue to QCD Matter and Multistage Collision Inference to relate pressure, energy density, and conserved-charge response.

References

• Arnold, Peter, Guy D. Moore, and Laurence G. Yaffe. “Effective Kinetic Theory for High Temperature Gauge Theories.” Journal of High Energy Physics 2003, no. 1 (2003): 030. DOI.