Effective Field Theory for Superconducting Phase Transitions

TL;DR

This paper develops an effective field theory for superconducting phase transitions using the Schwinger-Keldysh formalism, capturing dissipative and fluctuation effects near the critical point, and validates it through holographic methods.

Contribution

It introduces a symmetry-constrained effective field theory framework for superconductors, incorporating higher-order effects and validating it with holographic techniques.

Findings

Reproduces Ginzburg-Landau equations when truncated

Higgs mode is overdamped near the critical point

Holographic analysis reveals complex relaxation dynamics

Abstract

Employing the Schwinger-Keldysh formalism, we formulate an effective field theory for s-wave superconducting phase transition, where the dynamical variables consist of electromagnetic gauge field and complex scalar order parameter. Symmetry-constrained effective action allows systematic handling of dissipations and fluctuations. In particular, we explore the physical implications of higher-order terms, including those involving additional dynamical fields as well as higher time derivatives, on the real-time dynamics near the superconducting critical point. When appropriately truncated, the effective field theory reproduces the phenomenological Ginzburg-Landau equations. Upon crossing the critical temperature into the low-temperature phase, the electromagnetic gauge symmetry undergoes spontaneous breaking induced by the condensate of the order parameter. Collective excitation analysis reveals that the Higgs mode behaves as an overdamped diffusive mode near the critical point, while the phase fluctuation is absorbed into the gauge field via the Higgs mechanism. Via the holographic Schwinger-Keldysh technique, rigorous validation in a holographic superconductor confirms the structure of the effective action and quantifies the Wilsonian coefficients. Holographic results revaeal a complex relaxation parameter that indicates oscillatory dynamics characteristic of strongly coupled systems.