Quantum periods and TBA-like equations for a class of Calabi-Yau 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.

Bootstrapping Calabi–Yau quantum mechanics

“…In this paper, we apply the bootstrap method to the class of quantum mechanics systems derived from the mirror curves of some well known local toric Calabi-Yau geometries, where the Hamiltonians are exponential functions of both canonical position and momentum operators. The relations between quantum periods and TBA-like equations for these Calabi-Yau geometries are also recently studied in [19]. The quantization of mirror curves and the relation to topological string theory have been long considered e.g.…”