# Lessons from SU(N) Seiberg-Witten Geometry

### APA

Nardoni, E. (2022). Lessons from SU(N) Seiberg-Witten Geometry. Perimeter Institute. https://pirsa.org/22050069

### MLA

Nardoni, Emily. Lessons from SU(N) Seiberg-Witten Geometry. Perimeter Institute, Jun. 06, 2022, https://pirsa.org/22050069

### BibTex

@misc{ pirsa_PIRSA:22050069, doi = {10.48660/22050069}, url = {https://pirsa.org/22050069}, author = {Nardoni, Emily}, keywords = {Mathematical physics}, language = {en}, title = {Lessons from SU(N) Seiberg-Witten Geometry}, publisher = {Perimeter Institute}, year = {2022}, month = {jun}, note = {PIRSA:22050069 see, \url{https://pirsa.org}} }

University of Tokyo

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Abstract

"Motivated by applications to soft supersymmetry breaking, we revisit the Seiberg-Witten solution for N=2 super Yang-Mills theory in four dimensions with gauge group SU(N). We present a simple exact Taylor series expansion for the periods obtained at the origin of moduli space, thereby generalizing earlier results for SU(2) and SU(3). With the help of these analytic results and others, we analyze the global structure of the Kahler potential, presenting evidence for a conjecture that the unique global minimum is the curve at the origin of moduli space.
Two applications of these results are considered. Firstly, we analyze candidate walls of marginal stability of BPS states on special slices for which the expansions of the periods simplify. Secondly, we consider soft supersymmetry breaking of the N=2 theory to non-supersymmetric four-dimensional SU(N) gauge theory with two massless adjoint Weyl fermions (""adjoint QCD""). The Seiberg-Witten Kahler potential and strong coupling spectrum play a crucial role in this analysis, which ultimately leads to an exploration of the adjoint QCD phase diagram."