Revisiting the multi-monopole point of SU(N) N=2 gauge theory in four dimensions

Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) N = 2 gauge theory in four dimensions. At this point N -1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D'Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N, finding exact agreement with our first calculation.

Automated summary

Motivated by applications to soft supersymmetry breaking, this paper revisits the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) N = 2 gauge theory. The leading threshold corrections to the logarithmic running are explicitly calculated, with comparison made to existing literature and agreement found across various results. The results of Douglas and Shenker are also extended to finite N, showing exact agreement with the initial calculation.