The Second Sound of SU(2)

TL;DR

This paper uses the AdS/CFT correspondence to analytically compute transport coefficients like second sound speed, conductivity, and diffusion constants in a strongly interacting SU(2) system near a phase transition, highlighting similarities with other vector order systems.

Contribution

It provides the first analytical calculation of second sound and related transport properties in a non-abelian SU(2) system near a second order phase transition using holography.

Findings

Analytical expression for second sound speed near transition

Determination of conductivity and diffusion constants

Comparison with p-wave superconductors and helium-3

Abstract

Using the AdS/CFT correspondence, we calculate the transport coefficients of a strongly interacting system with a non-abelian SU(2) global symmetry near a second order phase transition. From the behavior of the poles in the Green's functions near the phase transition, we determine analytically the speed of second sound, the conductivity, and diffusion constants. We discuss similarities and differences between this and other systems with vector order parameters such as p-wave superconductors and liquid helium-3.