Goldstone modes in the emergent gauge fields of a frustrated magnet

We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focusing on the nearest-neighbor pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a \mathrm{U}(1)emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are...