1307.2691 (Jihye Sofia Seo)

Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A
Review    [PDF]

Jihye Sofia Seo

In this review, we consider the case where electrons, magnetic monopoles, and dyons become massless. Here we consider the ${\cal N} = 2$ supersymmetric Yang-Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1), SO(2r), Sp(2r), and SO(2r+1). which are studied by Riemann surfaces called Seiberg-Witten curves. We discuss physical singularity associated with massless particles, which can be studied by geometric singularity of vanishing 1-cycles in Riemann surfaces in hyperelliptic form. We pay particular attention to the cases where mutually non-local states become massless (Argyres-Douglas theories), which corresponds to Riemann surfaces degenerating into cusps. We discuss non-trivial topology on the moduli space of the theory, which is reflected as monodromy associated to vanishing 1-cycles. We observe how dyon charges get changed as we move around and through singularity in moduli space.

View original: http://arxiv.org/abs/1307.2691