PreprintCC BY 4.0arXiv
Algebraic Proofs of Quantum Period--TBA Relations
Abstract
We give algebraic proofs of two conjectural relations between quantum A-periods and thermodynamic Bethe ansatz (TBA)-like equations for quantum mirror curves. The quadratic relation follows from constant terms of shifted product expansions. For higher-degree relations, a cyclic quantum-torus trace and a finite matrix determinant identify the period with the free energy of nonoverlapping rods. Their density equation yields the TBA-like equation, with normalization fixed by the rod length. Both proofs hold as formal power series in the complex structure parameter, with exact dependence on q=eiℏ.
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BibTeX
@misc{huang2026algebraic,
title = {{Algebraic Proofs of Quantum Period--TBA Relations}},
author = {Min-xin Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09922},
eprint = {2610.09922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09922},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algebraic Proofs of Quantum Period--TBA Relations
AU - Min-xin Huang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09922
UR - https://arxiv.org/abs/2610.09922
AB - We give algebraic proofs of two conjectural relations between quantum A-periods and thermodynamic Bethe ansatz (TBA)-like equations for quantum mirror curves. The quadratic relation follows from constant terms of shifted product expansions. For higher-degree relations, a cyclic quantum-torus trace and a finite matrix determinant identify the period with the free energy of nonoverlapping rods. Their density equation yields the TBA-like equation, with normalization fixed by the rod length. Both proofs hold as formal power series in the complex structure parameter, with exact dependence on q=e^iℏ.
ER -