Stochastic Wess-Zumino-Witten model over a symplectic manifold

Abstract Over the path space of a symplectic manifold with end points in two Lagrangian submanifolds, we define a measure and a stochastic symplectic action in the simply connected case. We define a regularized Wess-Zumino-Witten Laplacian over the forms of finite degree over the path space. We perform a short time asymptotic near the critical points and find a limit Brownian harmonic oscillator: we can diagonalize it explicitly, and find the limit ground state of the Laplacian. We define a stochastic Witten complex, and its algebraic counterpart at the level of Chen forms.