The structure of supercooled liquids and glasses as Skyrmionic texture

A re-appraisal of the frustration models for glass-forming and supercooled liquids is presented. It is shown that the elasticity theory expressed by covariant derivatives with respect to an ideal template on a three-sphere S3S3 allows for the formation of localized soft Skyrmion states. Owing to the homomorphism between the proper rotation group SO(4) for the symmetry of S3S3 and the SU(2) group for the unitary 2×22×2 matrices, the simplest version of the frustration models contain Skyrme’s hedgehog solution stabilized by the fixed gauge background from the covariant derivatives. The structure of glasses and supercooled liquids can be rendered as dense Skyrmionic matter which reproduces geometric frustration at larger length scales in an orientable continuum.