Seiberg-Witten for $Spin(n)$ with Spinors

TL;DR

The paper addresses the construction of Seiberg-Witten solutions for 4D $N=2$ Spin$(n)$ gauge theories with spinor matter in the range $n=9$–$14$ at $β=0$, extending prior results for lower $n$. It employs compactifications of the 6D $(2,0)$ D$_N$ theory on a 4-punctured sphere to realize many theories (with both untwisted and twisted punctures) and derives the corresponding Seiberg-Witten curves, Calabi–Yau geometries, and the holomorphic gauge-coupling dependence, including detailed invariant $k$-differentials. The study provides explicit SW data for Spin$(9)$–Spin$(12)$ and partially for Spin$(13)$ and Spin$(14)$ theories, while showing that five theories lack six-dimensional realizations. It also analyzes a rich web of S-dual descriptions, including various Sp-, SU-, and G$_2$-gauged SCFTs, clarifying how spinor matter modifies the Coulomb-branch geometry and duality structure. The results broaden the landscape of 4D $N=2$ dualities from higher-dimensional constructions and delineate the limitations of 6D realizations for these Spin theories.

Abstract

$\mathcal{N}=2$ supersymmetric $Spin(n)$ gauge theory admits hypermultiplets in spinor representations of the gauge group, compatible with $β\leq0$, for $n\leq 14$. The theories with $β<0$ can be obtained as mass-deformations of the $β=0$ theories, so it is of greatest interest to construct the $β=0$ theories. In previous works, we discussed the $n\leq8$ theories. Here, we turn to the $9\leq n\leq 14$ cases. By compactifying the $D_N$ (2,0) theory on a 4-punctured sphere, we find Seiberg-Witten solutions to almost all of the remaining cases. There are five theories, however, which do not seem to admit a realization from six dimensions.