2020/08/26 by Masaki Honda, Honda, Masaki
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.2008.11461
26 pages
arxiv created 2020/08/26 · openalex publication_date 2020/08/26 · arxiv updated 2020/08/27 · openalex created_date 2020/09/01 · openalex updated_date 2026/07/28
We study the zero mode solutions of a Dirac operator on a magnetized Riemann surface of higher genus. In this paper, we define a Riemann surface of higher genus as a quotient manifold of the Poincar\acutee upper half-plane by a congruence subgroup, especially Γ0(N). We present a method to construct basis of cusp forms since the zero mode solutions should be cusp forms. To confirm our method, we select a congruence subgroup of semiprime level and show the demonstration to some lower weights. In addition, we discuss Yukawa couplings and matrix regularization as applications.