Nambu-Goldstone modes in non-equilibrium systems from AdS/CFT correspondence

TL;DR

This paper studies the behavior of Nambu-Goldstone modes in non-equilibrium systems using AdS/CFT correspondence, revealing diffusive and linear dispersion relations in different states, which enhances understanding of symmetry breaking in dissipative quantum systems.

Contribution

It demonstrates the dispersion relations of Nambu-Goldstone modes in non-equilibrium states via holographic models, showing diffusive and linear behaviors and their analytic forms.

Findings

Nambu-Goldstone modes exhibit diffusive dispersion in equilibrium.

In non-equilibrium steady states, modes show linear dispersion.

Linear dispersion relations are analytically expressed in dual field theory.

Abstract

We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents ${\cal N} = 4$ supersymmetric Yang-Mills theory coupled to ${\cal N = 2}$ flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes shows a diffusive behavior in the dispersion relation, which agrees with that found with the effective field theory approach. We also study a non-equilibrium steady state which has a constant current flow in the presence of an external electric field. In a non-equilibrium steady state, we find that the Nambu-Goldstone modes shows a linear dispersion in the real part of the frequency in addition to the diffusive behavior. Moreover, we analyze the linear dispersion of the Nambu-Goldstone modes in the hydrodynamic approximation. As a result, we find that the linear dispersion can be written as the analytic functions of quantities in the dual field theory. Our results imply that such a linear dispersion is a characteristic behavior of Nambu-Goldstone modes in a non-equilibrium steady state.