Bosonization in d > 2 dimensions

I discuss in this talk a bosonization approach recently developed. It leads to the (exact) bosonization rule for fermion currents in d > 2 dimensions and also provides a systematic way of constructing the bosonic action in different regimes.Comment: Talk given at "Trends in Theoretical Physics, CERN - Santiago de Compostela - La Plata Meeting", La Plata, April 1997, 34 pages, late

Two-loop finiteness of D=2 supergravity

We establish two-loop (on shell) finiteness of certain supergravity theories in two dimensions. Possible implications of this result are discussedComment: 11 page

Relativistic particle dynamics in D=2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and $\tau$-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables $\lambda$ show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model.Comment: 11 page

Cauchy conformal fields in dimensions d>2

Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined everywhere once we know their value on a codimension 1 surface. We classify all the unitary Cauchy fields. By analyzing the mode expansion on the unit sphere, we show that all unitary Cauchy fields are free in the sense that their correlation functions factorize on the 2-point function. We also discuss the possibility of non-unitary Cauchy fields and classify them in d=3 and 4.Comment: 45 pages; v2: references adde