Higgs/amplitude mode dynamics from holography

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.

Automated summary

Second order phase transitions are driven by an order parameter that becomes trivial at the critical point. At the same time, collective excitations involving the amplitude of the order parameter develop a gap that smoothly closes to zero at criticality. We develop analytical techniques to study the Higgs mode in holographic systems undergoing continuous phase transitions at finite temperature and chemical potential, allowing us to examine 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 determined by the black hole horizon data.