Related papers: S-duality, triangle groups and modular anomalies i…
We use localization techniques to study the non-perturbative properties of an N=2 superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the…
We determine the vacuum structure of N=2 supersymmetric QCD with fundamental quarks for gauge groups SO(n) and Sp(2n), extending prior results for SU(n). The solutions are all given in terms of families of hyperelliptic Riemann surfaces of…
The $S$-duality group $\mathbb{S}(\mathcal{F})$ of a 4d $\mathcal{N}=2$ supersymmetric theory $\mathcal{F}$ is identified with the group of triangle auto-equivalences of its cluster category $\mathscr{C}(\mathcal{F})$ modulo the subgroup…
We analyze the Coulomb phase of theories of $N=2$ SQCD with $SU(N_c)$ gauge groups which are conjectured to have exact electric-magnetic duality. We discuss the duality transformation of the particle spectrum, emphasizing the differences…
We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory…
We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…
We point out that for N=4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with…
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…
We determine the exact global structure of the moduli space of $N{=}2$ supersymmetric $SO(n)$ and $\USp(2n)$ gauge theories with matter hypermultiplets in the fundamental representations, using the non-renormalization theorem for the Higgs…
We work out Seiberg-like dualities for 3d $\mathcal{N}=2$ theories with SU(N) gauge group. We use the $SL(2,\mathbb{Z})$ action on 3d conformal field theories with U(1) global symmetry. One of generator S of $SL(2,\mathbb{Z})$ acts as…
We consider $\mathcal{N}=2$ supersymmetric $\text{SU}(2)$ gauge theory with $N_f=4$ massive hypermultiplets. The duality group of this theory contains transformations acting on the UV-coupling $\tau_{\text{UV}}$ as well as on the running…
We revisit the study of singular points in the Coulomb branch of $\mathcal{N}=2$ SQCD in four dimensions with gauge group $SU(N)$ and odd number of flavors. For certain choices of the mass parameters these vacua are not lifted by a mass…
We consider the low-energy effective action for the Coulomb phase of an $N = 2$ supersymmetric gauge theory with a rank one gauge group. The $N = 2$ superspace formalism is naturally invariant under an $SL(2, {\bf Z})$ group of duality…
$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the…
We propose an electric-magnetic duality and conjecture an exact conformal window for a class of non-supersymmetric U(N_c) gauge theories with fermions in the (anti)symmetric representation of the gauge group and N_f additional scalar and…
Seiberg and Witten have shown that in N=2 SQCD with $N_f=2N_c=4$ the S-duality group PSL(2,Z) acts on the flavor charges, which are weights of Spin(8), by triality. There are other N=2 SCFTs in which SU(2) SYM is coupled to…
We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation…
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…
We determine the mass dependence of the coupling constant for N=2 SYM with N_f=1,2,3 and 4 flavours. All these cases can be unified in one analytic expression, given by a Schwarzian triangle function. Moreover we work out the connection to…
We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular,…