Note on Quantum Periods and a TBA-like System

TL;DR

This paper explores the connection between quantum periods of a specific Calabi-Yau space and a TBA system related to ABJM theory, proposing a generalization and deriving associated differential operators and equations.

Contribution

It introduces a one-parameter generalization of the quantum period and TBA relation, and derives differential operators and equations in various limits.

Findings

Established a generalized relation between quantum periods and TBA systems.

Derived differential operators for quantum periods.

Formulated TBA-like equations in different limits.

Abstract

There is an interesting relation between the quantum periods on a certain limit 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-parameter generalization of the relation. Furthermore, we derive the differential operators for quantum periods and the TBA-like equation in various limits of the generalized relation.