Genus 2 Seiberg-Witten curves for rank 2 N=4 superYang-Mills theories

TL;DR

This paper constructs new genus 2 Seiberg-Witten curves for rank 2 N=4 superYang-Mills theories, aligning their conformal manifolds with S-duality predictions and clarifying their relation to integrable system spectral curves.

Contribution

It introduces explicit genus 2 curves for these theories using automorphism twists and clarifies their connection to S-duality and previous spectral curve constructions.

Findings

Conformal manifolds match S-duality predictions

Identified the correct sublattice projection for Coulomb branch geometry

Spectral curves of integrable systems do not directly apply to these theories

Abstract

We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute 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 $so(5) \simeq sp(4)$ 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.