SCALING BEHAVIOR IN STRING THEORY

In Calabi-Yau compactifications of the heterotic string there exist qu antities which are universal in the sense that they are present in eve ry Calabi-Yau string vacuum. It is shown that such universal character istics provide numerical information, in the form of scaling exponents , about the space of ground states in string theory. The focus is on t wo physical quantities. The first is the Yukawa coupling of a particul ar antigeneration, induced in four dimensions by virtue of supersymmet ry. The second is the partition function of the topological sector of the theory, evaluated on the genus-one worldsheet, a quantity relevant for quantum mirror symmetry and threshold corrections. It is shown th at both these quantities exhibit scaling behavior with respect to a ne w scaling variable and that a scaling relation exists between them as well.