Strong Coupling N=2 Gauge Theory with Arbitrary Gauge Group

TL;DR

This work provides a complete, representation‑independent construction of Seiberg–Witten data for pure $N=2$ gauge theories with arbitrary gauge group by explicitly defining the cycles on the Martinec–Warner spectral curve and the meromorphic differential $oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{oldsymbol{}}}}}}}$. It shows that strong-coupling monodromies arise from massless dyons whose charges lie in the co‑root lattice and that these dyons reproduce the weak‑coupling monodromies via duality, satisfying the Dirac–Schwinger–Zwanziger condition. The analysis extends to non‑simply‑laced groups using twisted affine algebras and outer automorphisms, maintaining a consistent democracy of dyons across coupling regimes. Together, the results place the Martinec–Warner construction on firmer footing and provide concrete tests linking perturbative spectra to nonperturbative monodromies for all simple gauge groups.

Abstract

A complete definition of the cycles, on the auxiliary Riemann surface defined by Martinec and Warner for describing pure N=2 gauge theories with arbitrary group, is provided. The strong coupling monodromies around the vanishing cycles are shown to arise from a set of dyons which becomes massless at the singularities. It is shown how the correct weak coupling monodromies are reproduced and how the dyons have charges which are consistent with the spectrum that can be calculated at weak coupling using conventional semi-classical methods. In particular, the magnetic charges are co-root vectors as required by the Dirac-Schwinger-Zwanziger quantization condition.

Figures (4)

• Figure 1: Definition of contours $A_i^a$ and $C$
• Figure 2: Choice of contours $A_i^1$ for $g=A_3$
• Figure 3: Action of outer automorphism on $D_4$ giving $G_2$
• Figure 4: Choice of contours for $G_2$