A Family of N=2 Gauge Theories with Exact S-Duality

TL;DR

This paper investigates an infinite family of $N=2$ $Sp(2n)$ gauge theories with four fundamental and one antisymmetric hypermultiplets, proposed to possess an exact $SO(8)\sdtimes SL(2,Z)$ duality in the massless limit. The authors test this by semiclassically quantizing monopole moduli spaces to derive the BPS/dyonic spectrum in both generic and aligned Higgs vacua, showing consistency with duality through reductions to known $N=4$ and scale-invariant $N=2$ results. A central technical development is the index-bundle framework for fermionic zero modes, which organizes bound-state spectra on monopole moduli spaces (including Taub-NUT), producing $SL(2,Z)$-invariant towers at each weight. The findings strongly support the proposed duality, while leaving open questions about higher-charge dyons and the full geometry of aligned-Higgs sectors on certain weights, suggesting rich links between string-theoretic realizations, nonperturbative field theory, and monopole dynamics.

Abstract

We study an infinite family of N=2 $Sp(2n)$ gauge theories that naturally arise from the D3-brane probe dynamics in F-theory. The matter sector consists of four fundamental and one antisymmetric tensor hyper multiplets. We propose that, in the limit of vanishing bare masses, the theory has exact $SO(8)\sdtimes SL(2,Z)$ duality. We examine the semiclassical BPS spectrum in the Coulomb phase by quantizing various monopole moduli space dynamics, and show that it is indeed consistent with the exact S-duality.