Postmodern String Theory: Stochastic Formulation

TL;DR

This paper develops a stochastic formulation of string dynamics, linking gauge theory, classical and quantum descriptions, and revealing a complex spacetime structure with Riemannian and Weyl geometries.

Contribution

It introduces a gauge-theoretic stochastic approach to string theory, connecting classical, semi-classical, and quantum formulations, and uncovers a multi-phase spacetime geometry.

Findings

Equivalence of stochastic approach to Carathéodory formulation of Nambu-Goto action.

Classical field equations as semi-classical limit of string wave equation.

Spacetime exhibits multi-phase structure with Riemannian and Weyl domains.

Abstract

In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carath\'eodory formulation of the Nambu-Goto action, supplemented by an averaging procedure over the family of classical string world-sheets which are solutions of the equation of motion. In this new framework, the string geodesic field is reinterpreted as the Gibbs current density associated with the string statistical ensemble. Next, we show that the classical field equations derived from the string gauge action, can be obtained as the semi-classical limit of the string functional wave equation. For closed strings, the wave equation itself is completely analogous to the Wheeler-DeWitt equation used in quantum cosmology. Thus, in the string case, the wave function has support on the space of all possible spatial loop configurations. Finally, we show that the string distribution induces a multi-phase, or {\it cellular} structure on the spacetime manifold characterized by domains with a purely Riemannian geometry separated by domain walls over which there exists a predominantly Weyl geometry.