Genus 2 Seiberg-Witten curves for rank 2 N $$ \mathcal{N} $$ =4 superYang-Mills theories - Philip C. Argyres; Mario Martone; Zekai Yu (Journal of High Energy Physics)
Abstract We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N $$ \mathcal{N} $$ =4 superYang-Mills theories using the automorphism twist approach. The conformal manifolds of these curves agree with those predicted by S-duality orbits of global structures, and we use this to identify which of the two S-duality orbits of the so 5 ≃ sp 4 $$ \mathfrak{so}(5)\simeq \mathfrak{sp}(4) $$ superYang-Mills theory the genus-2 curve corresponds to. We also compare the curves to earlier constructions of Seiberg-Witten curves for these theories as spectral curves of integrable systems. These spectral curves have genus greater than the rank, and so only give a Coulomb branch geometry upon projection to a sublattice of the homology lattice of the curves. We show how to determine the correct sublattice projection, and find that the integrable system curves do not apply to our theories.