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.

Brane Transitions from Exceptional Groups

“…It is interesting to investigate a direct relation between the brane configurations and the Painlevé equations. This may lead us to understand the relations between the ABJM matrix model and the Painlevé equation [45,46], the integrable hierarchy [47][48][49][50], the chiral projection [51][52][53] or the TBA system [20,54,55] more systematically.…”