Wilson loops, holomorphic anomaly equations and blowup equations

2023/05/16 by Xin Wang, Wang, Xin · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2305.09171

openalex publication_date 2023/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the topological string correspondence of the five-dimensional half-BPS Wilson loops on S¹. First, we propose the refined holomorphic anomaly equations for the BPS sectors of the Wilson loop expectation values. We then solve these equations and obtain many non-trivial novel integral refined BPS invariants for rank-one models. By studying the Wilson loop expectation values around the conifold point, we obtain the quantum spectra of the quantum Hamiltonians of the associated integrable systems. Lastly, as an application, the study of this paper leads to a generalization of the blowup equations for arbitrary magnetic fluxes that satisfy the flux quantization condition.

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