2025/10/08 by Ito, Katsushi, Shu, Hongfei, Yang, Jingjing · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2510.06956
We study the deformed supersymmetric quantum mechanics with a polynomial superpotential with ℏ-correction. In the minimal chamber, where all turning points are real and distinct, it was shown that the exact WKB periods obey the \mathbb Z4-extended thermodynamic Bethe ansatz (TBA) equations of the undeformed potential. By changing the energy parameter above/below the critical points, the turning points become complex, and the moduli are outside of the minimal chamber. We study the wall-crossing of the \mathbb Z4-extended TBA equations by this change of moduli and show that the \mathbb Z4-structure is preserved after the wall-crossing. In particular, the TBA equations for the cubic superpotential are studied in detail, where there are two chambers (minimal and maximal). At the maximally symmetric point in the maximal chamber, the TBA system becomes the two sets of the D3-type TBA equations, which are regarded as the \mathbb Z4-extension of the A3/\mathbb Z2-TBA equation.