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Description
I show that multivalued fields are a powerful tool to describe magnetic monopoles, vortex, and defect lines in condensed matter, and the associated phase transitions of confinement, superfluidity, and superconductivity. Also the geometric description of gravity can be formulated as a defect theory in a fictitious 'world crystal'. The rules of minimal electromagnetic and gravitational coupling are shown to be a consequence of a higher symmetry: multivalued gauge invariance of physical laws.