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A bstract We consider the Seiberg-Witten solution of pure $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions, with gauge group SU( N ). A simple exact series expansion for the dependence of the 2( N − 1) Seiberg-Witten periods a I ( u ) , a DI ( u ) on the N − 1 Coulomb-branch moduli u n is obtained around the ℤ 2 N -symmetric point of the Coulomb branch, where all u n vanish. This generalizes earlier results for N = 2 in terms of hypergeometric functions, and for N = 3 in terms of Appell functions. Using these and other analytical results, combined with numerical computations, we explore the global structure of the Kähler potential K = $$ \frac{1}{2}{\sum}_I $$ 1 2 ∑ I Im( $$ \overline{a} $$ a ¯ I a DI ), which is single valued on the Coulomb branch. Evidence is presented that K is a convex function, with a unique minimum at the ℤ 2 N -symmetric point. Finally, we explore candidate walls of marginal stability in the vicinity of this point, and their relation to the surface of vanishing Kähler potential. 

A bstract We present new families of AdS 5 solutions in M-theory preserving 4d $$ \mathcal{N} $$ N = 2 supersymmetry. We perform a systematic analysis of holographic observables for these solutions, providing evidence for an interpretation in terms of 4d superconformal field theories (SCFTs) of Argyres-Douglas type, realized in class $$ \mathcal{S} $$ S via a sphere with one irregular, and one regular puncture. The gravity solutions exhibit internal M5-brane sources that correspond to the irregular puncture. For a family of solutions, we identify explicitly the class $$ \mathcal{S} $$ S puncture data and perform a detailed match, including Higgs branch operators. For other families we comment on proposed field theory duals, based on irregular punctures labeled by nested Young tableaux. 

A bstract We initiate a study of the holographic duals of a class of four-dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories that are engineered by wrapping M5-branes on a sphere with an irregular puncture. These notably include the strongly-coupled field theories of Argyres-Douglas type. Our solutions are obtained in 7d gauged supergravity, where they take the form of a warped product of AdS 5 and a “half-spindle.” The irregular puncture is modeled by a localized M5-brane source in the internal space of the gravity duals. Our solutions feature a realization of supersymmetry that is distinct from the usual topological twist, as well as an interesting Stückelberg mechanism involving the gauge field associated to a generator of the isometry algebra of the internal space. We check the proposed duality by computing the holographic central charge, the flavor symmetry central charge, and the dimensions of various supersymmetric probe M2-branes, and matching these with the dual Argyres-Douglas field theories. Furthermore, we compute the large- N ’t Hooft anomalies of the field theories using anomaly inflow methods in M-theory, and find perfect agreement with the proposed duality. 

A bstract Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU( N ) $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions. At this point N − 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large- N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N , finding exact agreement with our first calculation.