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We discuss reductions of general N=1 four dimensional gauge theories on S^2. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an N=(0,2) gauge theory. As an application of our general observations, we discuss reductions of N=1 and N=2 dualities and argue that they imply certain two dimensional dualities.
We propose a generalization of S-folds to 4d $mathcal{N}=2$ theories. This construction is motivated by the classification of rank one 4d $mathcal{N}=2$ super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a configuration
We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. Our result fo
In the reduction of 4d dualities to 3d there are non-perturbative effects arising from monopoles acting as instantons. This mechanism has been reproduced in string theory by engineering the theories in a IIA brane setup. Nevertheless there are limiti
We study $N=2$ supersymmetric gauge theories on a large family of squashed 4-spheres preserving $SU(2)times U(1)subset SO(4)$ isometry and determine the conditions under which this background is supersymmetric. We then compute the partition function
In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 $mathcal{N}=2$ SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $mathcal{N}=2$ SCFTs. The glob