Quantum Periods and TBA-like Equations for a Class of Calabi-Yau Geometries

TL;DR

This paper explores the connection between quantum periods and TBA-like difference equations in Calabi-Yau geometries, introducing two derivation methods and expanding the class of geometries studied.

Contribution

It generalizes previous work to a broader class of Calabi-Yau geometries using two distinct derivation methods for TBA-like equations.

Findings

Two methods to derive TBA-like equations are presented.

The methods provide different realizations linked to the same quantum period.

The study extends the relation between quantum periods and TBA equations to more geometries.

Abstract

We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev's quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.