Perturbative gravitational couplings and Siegel modular forms in $D=4,N=2$ string models

TL;DR

This paper explores four-parameter four-dimensional N=2 string models, expressing their gravitational couplings using Siegel modular forms, revealing deep connections between string theory and modular mathematics.

Contribution

It introduces a novel expression of perturbative gravitational couplings in N=2 string models through Siegel modular forms, linking string theory with advanced modular functions.

Findings

Explicit formulas for gravitational couplings in specific models

Connection between Hodge numbers and modular forms

Potential implications for string dualities and compactifications

Abstract

We consider four-parameter $D=4,N=2$ string models with Hodge numbers $(4,214- 12n)$ and $(4,148)$, and we express their perturbative Wilsonian gravitational coupling $F_1$ in terms of Siegel modular forms.