Quantum periods and TBA-like equations for a class of Calabi-Yau geometries
Bao-ning Du (Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui, 230026, China, Peng Huanwu Center for Fundamental Theory, Hefei, Anhui, 230026, China); Min-xin Huang (Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui, 230026, China, Peng Huanwu Center for Fundamental Theory, Hefei, Anhui, 230026, China)
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.