TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917480499249152 |
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| author | Peng, Feiyu Shu, Hongfei |
| author_facet | Peng, Feiyu Shu, Hongfei |
| contents | We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the subdominant solutions, we construct the Q-/Y-systems and derive the corresponding TBA equations. The dependence of the moduli parameters is found to be encoded in the boundary conditions of the Y-functions at $θ\to -\infty$. From these boundary data, we derive an analytic expression for the effective central charge, which also governs the subleading contribution in the large-$θ$ expansion of the TBA equations. Finally, we compare the large-$θ$ expansion of the Q-function derived from the TBA equations with that obtained from the WKB method, which yields analytic agreement at subleading order and precise numerical agreement at the higher-order corrections. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_27794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation Peng, Feiyu Shu, Hongfei High Energy Physics - Theory Mathematical Physics We develop the ODE/IM correspondence for the higher-order Mathieu equation arising from the quantum Seiberg-Witten curve of the pure $SU(r+1)$ ${\cal N}=2$ supersymmetric Yang-Mills theory. From the subdominant solutions, we construct the Q-/Y-systems and derive the corresponding TBA equations. The dependence of the moduli parameters is found to be encoded in the boundary conditions of the Y-functions at $θ\to -\infty$. From these boundary data, we derive an analytic expression for the effective central charge, which also governs the subleading contribution in the large-$θ$ expansion of the TBA equations. Finally, we compare the large-$θ$ expansion of the Q-function derived from the TBA equations with that obtained from the WKB method, which yields analytic agreement at subleading order and precise numerical agreement at the higher-order corrections. |
| title | TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.27794 |