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There is an interesting relation between the quantum periods on a certainlimit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and a TBA(Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM(Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parametergeneralization of the relation. Furthermore, we derive the differentialoperators for quantum periods and the TBA-like equation in various limits ofthe generalized relation.

Note on Quantum Periods and a TBA-like System