Condensed matter systems can possess striking parallels with gauge theories that arise in the context of high-energy physics, exemplified by the Anderson-Higgs transition in superconductors , and emergent photons  and magnetic monopoles  in spin ice. Such examples raise the question of where else there is potential for low-energy experiments to inform physics relevant to high-energy scales.
Here, we present two further parallels that exist between the excitations of magnetic systems and two of nature's fundamental gauge theories, namely electrodynamics and general relativity.
We first review the connection between the Goldstone modes of a Néel antiferromagnet and the photons of electromagnetism. Then, motivated by results from simulation, we present a mapping between the linearly dispersing Goldstone modes of a system with ferroquadrupolar (spin-nematic) order and gravitational waves in flat space, as described within the framework of linearized gravity. Our results suggest that the massless spin-2 excitations of spin-nematic phases could provide a low-energy analogue of gravitational waves.
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