Scaling Behavior in String Theory

TL;DR

This paper investigates universal scaling behaviors in Calabi-Yau string compactifications, revealing how key physical quantities like Yukawa couplings and partition functions scale and relate, providing insights into the structure of string vacua.

Contribution

It introduces the concept of universal scaling exponents in string theory and demonstrates their relation to physical quantities across all Calabi-Yau vacua.

Findings

Yukawa couplings exhibit specific scaling behavior.

Partition functions show universal scaling properties.

A scaling relation links the Yukawa coupling and partition function.

Abstract

In Calabi--Yau compactifications of the heterotic string there exist quantities which are universal in the sense that they are present in every Calabi--Yau string vacuum. It is shown that such universal characteristics provide numerical information, in the form of scaling exponents, about the space of ground states in string theory. The focus is on two physical quantities. The first is the Yukawa coupling of a particular antigeneration, induced in four dimensions by virtue of supersymmetry. 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 that both these quantities exhibit scaling behavior with respect to a new scaling variable and that a scaling relation exists between them as well.