Exponential concentration for quantum periods via mirror symmetry

TL;DR

This paper demonstrates that quantum periods of certain Fano manifolds exhibit exponential concentration, extending properties of hypergeometric series through mirror symmetry and geometric analysis.

Contribution

It establishes exponential concentration for quantum periods of Fano manifolds with specific Landau-Ginzburg models, linking hypergeometric series and mirror symmetry.

Findings

Quantum periods of Fano manifolds have exponential concentration.

Suitable modifications of hypergeometric series preserve exponential concentration.

Quantum periods share this property when the manifold admits a weak Landau-Ginzburg model.

Abstract

We investigate power series satisfying the exponential concentration property, and show that suitable modifications of hypergeometric series respect this property. As a geometric application, we prove that the quantum period of a Fano manifold possesses the same property, whenever the manifold admits a convenient weak Landau-Ginzburg model with non-negative coefficients.