2005-11-04

Note unusual time and location: 10:10-11 am, 206 Malott Hall

Jonathan Weitsman, University of California at Santa Cruz

Measures on Banach manifolds, Random surfaces, and nonperturbative string theory

Let $\mu$ be Gaussian measure of covariance $(\sqrt{\Delta+m^2})^{-1}$ on the circle, where $m\geq 0$. Using techniques of L. Gross we construct a probability measure $\nu$ on $L_2(\mu)$ whose expectations compute correlation functions in free bosonic string theory. We next construct a function $V\in L_p(\nu)$ for all $p>1$ such that

Z(\lambda):=\int d\nu\exp(i\lambda V)

is a $C^\infty$ function whose power series expansion computes the partition function of interacting bosonic string theory. Similar results hold for correlation functions. We conjecture that the terms arising in this power series expansion correspond to the Polyakov measure on the moduli of curves.