Interacting theory of collective and topological fields in 2 dimensions

Abstract

We propose a generalization of the collective field theory hamiltonian, including interactions between the original bosonic collective field w 0( z) and supplementary fields w j (z) realizing classically a w ∞ algebra. The latter are then shown to represent a 3-dimensional topological field theory. This generalization follows from a conjectured representation of the W 1+∞ algebra of bilinear fermion operators underlying the original matrix model. It provides an improved bosonization scheme for (1+1)-dimensional fermion theories.