Magnetized Riemann Surface of Higher Genus and Eta Quotients of Semiprime Level

Abstract

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 Poincaré upper half-plane by a congruence subgroup, especially Γ 0 (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.

Vector bundles on fuzzy Kähler manifolds

“…See[17] for the analysis of Dirac operator zero modes of Riemann surfaces with higher genera, where the zero modes have more complex representations than those of CP 1 = S 2 and T 2 .…”