2020/12/17 by Sibasish Banerjee, Banerjee, Sibasish, Pietro Longhi +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2012.09769
openalex publication_date 2020/12/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study BPS states of 5d N=1 SU(2) Yang-Mills theory on S1× ℝ4. Geometric engineering relates these to enumerative invariants for the local Hirzebruch surface \mathbbF0. We illustrate computations of Vafa-Witten invariants via exponential networks, verifying fiber-base symmetry of the spectrum at certain points in moduli space, and matching with mirror descriptions based on quivers and exceptional collections. Albeit infinite, parts of the spectrum organize in families described by simple algebraic equations. Varying the radius of the M-theory circle interpolates smoothly with the spectrum of 4d N=2 Seiberg-Witten theory, recovering spectral networks in the limit.