S-duality in N=2 supersymmetric gauge theories

TL;DR

The paper addresses infinite-coupling points in four-dimensional N=2 gauge theories by proposing a generalized S-duality: at infinite coupling, a theory with gauge group H is equivalent to a weakly-coupled theory with a smaller gauge group G coupled to an isolated rank (r-s) N=2 SCFT whose flavor symmetry H is partially gauged. The authors support this framework by analyzing Seiberg-Witten curves and beta-functions in explicit examples, showing that infinite-coupling limits correspond to weakly coupled dual frames containing SCFT sectors, such as rank-1 E6 and E7 theories, with exact flavor-current central charges computed via embedding-index beta-function matching. The SU(3) with six fundamentals dual to SU(2) with the E6 SCFT and the Sp(2) with 12 half-hypermultiplets dual to SU(2) with the E7 SCFT provide concrete tests, yielding k_E6 = 6 and k_E7 = 8 and demonstrating coupling-independence of these central charges. The results extend S-duality to N=2 theories, reveal nontrivial non-Lagrangian sectors in four dimensions, and furnish exact data on the currents of isolated SCFTs that can guide the classification and analysis of infinite-coupling phenomena. These insights enable a deeper understanding of how nonperturbative sectors couple to gauge dynamics and offer a systematic path to study other rank-two and higher theories with infinite-coupling points.

Abstract

A solution to the infinite coupling problem for N=2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E_6 and E_7 SCFTs are found as limits of Lagrangian field theories.