Effective field theory for dissipative photons from higher-form symmetries

TL;DR

This paper develops a symmetry-based effective field theory for dissipative photon dynamics in insulating media at finite temperature, integrating higher-form symmetries, Schwinger-Keldysh formalism, and thermodynamic consistency.

Contribution

It introduces a novel effective field theory framework that combines generalized symmetries with real-time formalism to describe dissipative photon behavior.

Findings

Derived the entropy current with non-negative divergence.

Ensured consistency with fluctuation-dissipation and Onsager relations.

Clarified the gauge redundancy origin via higher-form symmetries.

Abstract

Recent developments in generalized symmetries have provided new insights into quantum field theories. Within this framework, photons can be understood as Nambu-Goldstone modes associated with a spontaneously broken higher-form symmetry. In this work, we develop an effective field theory that builds on this symmetry structure to describe the real-time dynamics of photons in insulating media at finite temperature. Combining the Schwinger-Keldysh formalism with the generalized coset construction, we formulate a symmetry-based effective action that incorporates both conservative and dissipative effects. The effective theory implements the dynamical Kubo-Martin-Schwinger symmetry, ensuring consistency with the fluctuation-dissipation relation and Onsager's reciprocal relations. Within this framework, we derive the entropy current associated with dissipative photon dynamics and demonstrate the non-negativity of its divergence, in accordance with the second law of thermodynamics. We also clarify the symmetry origin of the gauge redundancy in the unbroken phase within the Schwinger-Keldysh framework, relating it to strong and weak realizations of higher-form symmetries. Our results provide a model-independent effective description of photon dynamics in insulating media at finite temperature.