Connections between some kinetic and equilibrium theories of the glass transition

Connections between the static density-functional theory of the glass transition and the dynamic mode-coupling theory of the glass transition are discussed. In three dimensions, some approximate equivalences are established. These equivalences are made more precise by examining high-dimensionality liquids and glasses. The similarities with early static and dynamic mean-field theories of the spin-glass transition are emphasized. Some speculations on the relationship between structural glasses and Potts glasses are also included.