2019/12/02 by Yang, Wenzhe
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1912.01121
In this paper, we will apply the tools from number theory and modular forms to the study of the Seiberg-Witten theory. We will express the holomorphic functions a, aD, which generate the lattice Z=ne a+nm aD, (ne, nm) ∈ ℤ2 of central charges, in terms of the periods of the Legendre family of elliptic curves. Thus we will be able to compute the transformations of the quotient aD/a under the action of the modular group PSL(2,ℤ). We will show the Schwarzian derivative of the quotient aD/a with respect to the complexified coupling constant is given by the theta functions. We will also compute the scalar curvature of the moduli space of the N=2 supersymmetric Yang-Mills theory, which is shown to be asymptotically flat near the perturbative limit.