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arXiv · 2608.15878

Lagrangian Schur index and Bethe ansatz type formula

Yutong Li·Yiwen Pan
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Abstract

We propose a surprisingly elementary method to compute the Schur index in closed-form for general $\mathcal{N} = 2$ Lagrangian theories. The method is inspired by the Bethe ansatz type formula for $\mathcal{N} = 1$ superconformal index. We identify issues underlying the original derivation: the loss of periodicity property upon integration and the omitted poles outside of the annulus region. We circumvent the problems and transform integration into solving a simple difference equation. The final result is expressed as a finite sum of quasi-Jacobi forms involving twisted Eisenstein series. We test our method on different types of theories, including BCD-type $\mathcal{N} = 4$ theories and various $\mathcal{N} = 2$ quiver gauge theories.

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Yutong Li, Yiwen Pan. 2026-08-16. Lagrangian Schur index and Bethe ansatz type formula. https://arxiv.org/abs/2608.15878

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