Effective field theory for dissipative photons from higher-form symmetries
Genki Yoshimura, Yukinao Akamatsu, Yuji Hirono
TL;DR
This work develops a finite-temperature effective field theory for photons arising from spontaneously broken U(1)^{[1]} 1-form symmetry, by merging the generalized coset construction with the Schwinger–Keldysh framework. The resulting DKMS-consistent action describes both conservative and dissipative photon dynamics in insulating media, and is shown to be equivalent to Langevin Maxwell equations with noise obeying fluctuation–dissipation relations. In D=3+1, the authors derive a general Lagrangian up to derivative order m+n≤4, featuring dissipative transport through τ_E and τ_B and parity-odd contributions such as the chiral magnetic effect under controlled symmetry conditions. They construct the entropy current with non-negative divergence and analyze electromagnetic duality within this dissipative SK EFT, providing a model-independent, symmetry-based description of thermal photon dynamics and laying groundwork for extensions to unbroken phases and higher-form fracton-like systems.
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.