0000000000924270
AUTHOR
Christian Fronsdal
Three-dimensional singletons
The three-dimensional analog of singleton gauge theory turns out to be related to the topological gauge theory of Schwartz and Witten. It is a fully-fledged gauge theory, though it involves only a single scalar field. Real, physical degrees of freedom propagate in 3-space, but they are ‘confined’ in the sense that they cannot be detected locally. The physical Hamiltonian density is not zero, but it is concentrated on the boundary at spatial infinity. This boundary surface, a torus, supports a two-dimensional conformal field theory.
THREE-D SINGLETONS AND 2-D C.F.T.
Two-dimensional Wess-Zumino-Novikov-Witten theory is extended to three dimensions, where it becomes a scalar gauge theory of the singleton type. The three-dimensional formulation involves a scalar field valued in a compact group G, a Nakanishi-Lautrup field valued in Lie (G) and Faddeev-Popov ghosts. The physical sector, characterized by the vanishing of the Nakanishi-Lautrup field, coincides with the WZNW theory of the group G. Three-dimensional space-time structure involves a generalized metric, but only its boundary values are of consequence. An alternative formulation in terms of left and right movers (in three dimensions!) is also possible.