Higgs/Amplitude Mode Dynamics From Holography

TL;DR

This paper develops analytical holographic techniques to study the Higgs mode near second order phase transitions, linking collective excitations to thermodynamic and black hole horizon data.

Contribution

It introduces a method to analyze the Higgs mode in holographic systems undergoing continuous phase transitions at finite temperature and chemical potential.

Findings

Green's functions expressed via thermodynamics and transport coefficients

Analytical description of Higgs mode gap closure at criticality

Connection between collective excitations and black hole horizon data

Abstract

Second order phase transitions are universally driven by an order parameter which becomes trivial at the critical point. At the same time, collective excitations which involve the amplitude of the order parameter develop a gap which smoothly closes to zero at criticality. We develop analytical techniques to study this "Higgs" mode in holographic systems which undergo a continuous phase transition at finite temperature and chemical potential. This allows us to study the linear response of the system at energy scales of the order of the gap. We express the Green's functions of scalar operators in terms of thermodynamic quantities and a single transport coefficient which we fix in terms of black hole horizon data.