Calabi–Yau attractor varieties and degeneration of Hodge structure

Abstract We present an application of asymptotic Hodge theory to the study of the attractor locus in flux compactifications. Our strategy is to investigate attractor points arising at the boundary of moduli spaces, where the limiting mixed Hodge structures encode the asymptotic geometry of degenerating Calabi–Yau varieties. By compactifying period domains of Hodge structures, we establish a solid framework for analyzing attractors at infinity and demonstrate that the boundary components provide a natural setting for their occurrence. The main result of this work is an effective method to characterize such boundary attractors, derived through explicit equations obtained from the asymptotic behavior of nilpotent orbits in period mappings. This approach integrates tools from asymptotic Hodge theory with computational techniques based on period vectors familiar from the physics of type IIB flux compactifications, thereby bridging algebraic-geometric and physical perspectives on the attractor mechanism. Beyond its mathematical formulation, the results presented here contribute directly to the theoretical understanding of flux vacua and moduli stabilization in string theory. The explicit boundary equations for attractor points describe fixed configurations of complex-structure moduli in the low-energy supergravity limit, offering a geometric interpretation of the extremization of the central charge and the stabilization of scalar fields in the BPS sector. Consequently, the asymptotic Hodge-theoretic framework developed here not only clarifies the geometric origin of attractor phenomena but also provides a rigorous mathematical model for physical stabilization mechanisms in compactified string and supergravity theories.