Abstract
A microscopic model is introduced, in which the two-level systems are due to the non-trivial topological structure of any glass. Glasses are punctured by Z 2 line defects (characterized by their oddness). Their free energy is of the Yang-Mills type, with both matter and gauge fields belonging to the rotation group SO(3). The gauge symmetry is associated with the local invariance or overall homogeneity of glasses. The solutions of the classical field equations belong to either of two distinct classes. The two classical solutions are related to each other by a gauge transformation: they can therefore tunnel into each other and yield the familia two-level systems responsible for the anomalous elementary excitations and low temperature properties of glasses.
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