On Field Theories of Loops

Abstract

We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in a field theory of loops. The corresponding Fokker-Planck hamiltonian defines a non-critical string field theory. We study both orientable and non-orientable interactions of loops in terms of matrix models and take the continuum limit for one-matrix case. As a consequence, we show the equivalence of stochastic quantization of matrix models in loop space to the transfer-matrix formalism in dynamical triangulation of random surfaces. We also clarifies the origin of Virasoro algebra in this context.