Calabi-Yau attractor varieties and degeneration of Hodge structure

TL;DR

This paper explores the geometric structure of flux compactifications in string theory on elliptic Calabi-Yau threefolds, focusing on attractor points and their relation to Hodge structure degeneration using advanced mathematical techniques.

Contribution

It introduces equations for the attractor locus in flux compactifications via asymptotic analysis of nilpotent orbits, blending Hodge theory and numerical period vectors.

Findings

Derived equations describing attractor points on boundary components.

Connected Hodge structure degeneration with flux compactification loci.

Applied asymptotic Hodge theory to string theory flux analysis.

Abstract

We study the structure of string theory flux compactification for a general family of elliptic CY 3-folds. We investigate the locus of the attractor points of the flux compactification in type IIB string theory on the boundary components of period domains. Specifically we give equations describing this locus through the asymptotic of nilpotent orbits on period domains. our approach is a mixture of techniques of asymptotic Hodge theory and the numerical period vectors used in physics.