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A bstract We consider the four-dimensional N = 2 quiver gauge theory arising from a ℤ 2 orbifold of N = 4 super Yang-Mills with gauge group SU(2 N ). We study the integrated correlator between a half-BPS Wilson line and two Higgs branch operators of conformal dimension 2. Using supersymmetric localization, we resum the perturbative series for this observable and obtain exact expressions for both the planar and next-to-planar terms of its large N expansion, valid for arbitrary values of the ’t Hooft coupling. Finally, through a combination of analytical and numerical methods, we determine the leading terms of the corresponding strong-coupling expansions.

A bstract We consider the 4 d N = 2 superconformal quiver gauge theory obtained by a ℤ 2 orbifold of N = 4 super Yang-Mills (SYM). By exploiting supersymmetric localization, we study the integrated correlator of two Coulomb branch and two moment map operators and the integrated correlator of four moment map operators, determining exact expressions valid for any value of the ’t Hooft coupling in the planar limit. Additionally, for the second correlator, we obtain an exact expression also for the next-to-planar contribution. Then, we derive the leading terms of their strong-coupling expansions and outline the differences with respect to the N = 4 SYM theory.

A bstract We consider two four-dimensional gauge theories with gauge group SU( N ): the N = 4 Super Yang-Mills (SYM) theory and the N = 2 quiver gauge theory obtained as a ℤ 2 orbifold of N = 4 SYM. In this context, we study a novel class of integrated correlators, namely those involving n -coincident Wilson lines and two moment map operators of conformal dimension two. By exploiting supersymmetric localization, we obtain exact expressions for these observables valid in the large- N limit. Furthermore, using a combination of analytical and numerical methods, we derive their strong coupling expansions.

A bstract We consider 4-dimensional N = 2 superconformal quiver theories with SU( N ) M gauge group and bi-fundamental matter and we evaluate correlation functions of n coincident Wilson loops in the planar limit of the theory. Exploiting specific untwisted/twisted combinations of these operators and using supersymmetric localization, we are able to resum the whole perturbative expansion and find exact expressions for these correlators that are valid for all values of the ’t Hooft coupling. Moreover, we analytically derive the leading strong coupling behaviour of the correlators, showing that they obey a remarkable simple rule. Our analysis is complemented by numerical checks based on a Padé resummation of the perturbative series.

A bstract We study the correlation function between one single-trace scalar operator and a circular Wilson loop in the 4 d N = 2 superconformal field theory with gauge group SU( N ) and matter transforming in the symmetric and anti-symmetric representations. By exploiting supersymmetric localization, we resum the perturbative expansion of this correlator in the large- N ’t Hooft limit. Furthermore, using both analytical and numerical techniques, we provide a prediction for the leading term of its strong coupling expansion and we compare this prediction to numerical Padé resummations of the perturbative series.

A bstract Even though for generic N = 1 theories it is not possible to separate distinct branches of supersymmetric vacua, in this paper we study a special class of N = 1 SCFTs, these of Class S k for which it is possible to define Coulomb and Higgs branches precisely as for the N = 2 theories of Class S from which they descend. We study the BPS operators that parameterise these branches of vacua using the different limits of the superconformal index as well as the Coulomb and Higgs branch Hilbert Series. Finally, with the tools we have developed, we provide a check that six dimensional (1 , 1) Little String theory can be deconstructed from a toroidal quiver in Class S k .

A bstract We consider the N = 2 quiver gauge theory arising from a ℤ M orbifold of N = 4 Super Yang-Mills theory. Over the years, exploiting supersymmetric localization, exact expressions for several observables have been derived in the planar limit of this theory. In particular, some of these can be expressed as Fredholm determinants of semi-infinite matrices and their strong coupling expansions in inverse powers of the ’t Hooft coupling have been calculated analytically to any desired order. On the other hand, there are also observables that cannot be rewritten in such a closed form, therefore extracting information at strong coupling is more complicated and almost no results are known beyond the leading order. In this work we focus on two observables of this type: the correlators of n coincident Wilson loops and the integrated correlators of two Higgs branch operators in the presence of a Wilson line. We introduce an analytic method to evaluate the first terms of their strong coupling expansions. We also outline a numerical algorithm that serves as an independent check of the analytical results and provides predictions in cases where analytical techniques are currently not known.

A bstract We present in the context of supersymmetric gauge theories an extension of the Weyl integration formula, first discovered by Robert Wendt [1], which applies to a class of non-connected Lie groups. This allows to count in a systematic way gauge-invariant chiral operators for these non-connected gauge groups. Applying this technique to O( n ), we obtain, via the ADHM construction, the Hilbert series for certain instanton moduli spaces. We validate our general method and check our results via a Coulomb branch computation, using three-dimensional mirror symmetry.

A bstract Using supersymmetric localization, we consider four-dimensional N = 2 superconformal quiver gauge theories obtained from ℤ n orbifolds of N = 4 Super Yang-Mills theory in the large N limit at weak coupling. In particular, we show that: 1) The partition function for arbitrary couplings can be constructed in terms of universal building blocks. 2) It can be computed in perturbation series, which converges uniformly for |λ I | < π 2 , where λ I are the ’t Hooft coupling of the gauge groups. 3) The perturbation series for two-point functions can be explicitly computed to arbitrary orders. There is no universal effective coupling by which one can express them in terms of correlators of the N = 4 theory. 4) One can define twisted and untwisted sector operators. At the perturbative orbifold point, when all the couplings are the same, the correlators of untwisted sector operators coincide with those of N = 4 Super Yang-Mills theory. In the twisted sector, we find remarkable cancellations of a certain number of planar loops, determined by the conformal dimension of the operator.

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