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This lecture explores the fascinating connection between fracton phases of matter and Carrollian fluids, delving into their unique properties and theoretical frameworks. Learn how fracton phases with mobility constraints can only achieve fluid description through spontaneous breaking of dipole symmetry, and how they couple to Aristotelian background geometries. Discover the construction of hydrostatic partition functions incorporating Goldstone bosons, leading to two distinct classes: p-wave and s-wave fracton superfluids. The presentation establishes important parallels between the fracton algebra and Carroll algebra, explaining how Carrollian fluids break boost symmetries spontaneously. This theoretical approach unifies previously disconnected concepts of Carrollian fluids, showing how the resulting Goldstone mode constructs an effective Aristotelian geometry that enables first-order hydrodynamics descriptions and generates a Horava-Lifshitz-like effective action for the boost Goldstone.
