N=2 dualities

TL;DR

The paper develops a unified, four-dimensional framework to study N=2 SCFTs via generalized quivers built from strongly interacting building blocks, extending S-duality and Argyres-Seiberg duality to SU(2), SU(3), and SU(N) quiver families. It relies on Seiberg-Witten curves realized as covers of punctured Riemann surfaces, whose moduli spaces align with Teichmüller spaces, and on twisted compactifications of 6D (2,0) theories on these surfaces with codimension-2 defects. By identifying puncture data with flavor symmetries and mass deformations, it derives explicit SW curves for each class (A1, A2, and beyond) and shows how various weakly coupled frames emerge at degeneration cusps. The work also proposes a four-dimensional definition of theories of N M5 branes wrapped on a Riemann surface, clarifying the role of defects and paving the way for extensions to D/E-type theories and richer brane constructions.

Abstract

We study the generalization of S-duality and Argyres-Seiberg duality for a large class of N=2 superconformal gauge theories. We identify a family of strongly interacting SCFTs and use them as building blocks for generalized superconformal quiver gauge theories. This setup provides a detailed description of the ``very strongly coupled'' regions in the moduli space of more familiar gauge theories. As a byproduct, we provide a purely four dimensional construction of N=2 theories defined by wrapping M5 branes over a Riemann surface.

Figures (43)

• Figure 1: Left: the space of gauge couplings $\tau$ modulo S-duality for $SU(2)$$N_f=4$. The weakly coupled region is at $\tau \to i \infty$. Right: the space of gauge couplings $\tau$ modulo S-duality for $SU(N)$$N_f=2N$. The weakly coupled region is at $\tau \to i \infty$. The very strongly coupled region at $\tau \to 1$
• Figure 2: Different useful ways to depict $SU(2)$ gauge theory with four fundamental flavors. On the left, a standard quiver diagram, where circles indicate gauge groups, and squares fundamental flavors; the four flavors have an $SO(8)$ flavor symmetry. In the middle, a quiver diagram where the four flavors have been split into two groups of two flavors; each group carries a $SO(4)=SU(2) \times SU(2)$ flavor symmetry. On the right, a generalized quiver diagram, depicting separately the two $SU(2)$ flavor groups for each pair of fundamentals
• Figure 3: The action of S duality on the four $SU(2)$ flavor subgroups: the three possible ways to pair them up into the $SO(4)$ symmetry of two fundamentals
• Figure 4: Left: (a) the space of gauge couplings $\tau$ modulo S-duality. Right: (b) the space of gauge couplings $\tau$ modulo S-duality transformations which do not permute the masses. At the three cusps $\tau = i \infty$, $\tau =0$, $\tau=1$ respectively, the weakly coupled description of the theory has flavor groups labeled as in fig. \ref{['fig:su2nf4sd']}
• Figure 5: The degeneration limits of a sphere with four marked punctures. They correspond to the three weak coupling limits of $SU(2)$$N_f=4$ depicted in fig \ref{['fig:su2nf4sd']}