Ellipsoid partition function from Seiberg-Witten monopoles

We study Higgs branch localization of N=2 supersymmetric theories placed on compact Euclidean manifolds. We analyze the resulting localization equations in detail on the four-sphere and find that in this case the path integral is dominated by vortex-like configurations as well as singular Seiberg-Witten monopoles located at the north and south pole. The partition function is written accordingly.Comment: 37 pages; v2: minor typos corrected, published versio

Schur correlation functions on S3×S1S^3\times S^1

The Schur limit of the superconformal index of four-dimensional $\mathcal N=2$ superconformal field theories has been shown to equal the supercharacter of the vacuum module of their associated chiral algebra. Applying localization techniques to the theory suitably put on $S^3\times S^1$, we obtain a direct derivation of this fact. We also show that the localization computation can be extended to calculate correlation functions of a subset of local operators, namely of the so-called Schur operators. Such correlators correspond to insertions of chiral algebra fields in the trace-formula computing the supercharacter. As a by-product of our analysis, we show that the standard lore in the localization literature stating that only off-shell supersymmetrically closed observables are amenable to localization, is incomplete, and we demonstrate how insertions of fermionic operators can be incorporated in the computation.Comment: 49 page

Intersecting Surface Defects and Instanton Partition Functions

We analyze intersecting surface defects inserted in interacting four-dimensional N = 2 supersymmetric quantum field theories. We employ the realization of a class of such systems as the infrared fixed points of renormalization group flows from larger theories, triggered by perturbed Seiberg-Witten monopole-like configurations, to compute their partition functions. These results are cast into the form of a partition function of 4d/2d/0d coupled systems. Our computations provide concrete expressions for the instanton partition function in the presence of intersecting defects and we study the corresponding ADHM model.Comment: 66 pages; v2: minor typos correcte

Higgs branch localization of N=1\mathcal{N}=1 theories on S3×S1S^3 \times S^1

We apply the method of Higgs branch localization to the $\mathcal{N}=1$ supersymmetric partition function on $S^3\times S^1.$ As a result, we show that it can be written as the product of an elliptic vortex and anti-vortex partition function summed over a finite number of Higgs vacua.Comment: 29 pages; v2: minor improvements, references adde

Argyres-Douglas Theories in Class S Without Irregularity

We make a preliminary investigation into twisted $A_{2n}$ theories of class S. Contrary to a common piece of folklore, we establish that theories of this type realise a variety of models of Argyres-Douglas type while utilising only regular punctures. We present an in-depth analysis of all twisted $A_2$ trinion theories, analyse their interrelations via partial Higgsing, and discuss some of their generalised S-dualities.Comment: 37 page

Deformation quantizations from vertex operator algebras

In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N=2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected subsector in the three-dimensional circle-reduced theory. We answer this question positively if the UV R-symmetries do not mix with accidental (topological) symmetries along the renormalization group flow from the four-dimensional theory on a circle to the three-dimensional theory. If they do mix, we still find a deformation quantization but at different values of its period.Comment: 40 pages; v2: argument in section 4.1 refined, references added; v3: minor improvements, published versio

New N=2 superconformal field theories from S-folds

We study the four-dimensional N=2 superconformal field theories that describe D3-branes probing the recently constructed N=2 S-folds in F-theory. We introduce a novel, infinite class of superconformal field theories related to S-fold theories via partial Higgsing. We determine several properties of both the S-fold models and this new class of theories, including their central charges, Coulomb branch spectrum, and moduli spaces of vacua, by bringing to bear an array of field-theoretical techniques, to wit, torus-compactifications of six-dimensional N=(1,0) theories, class S technology, and the SCFT/VOA correspondence.Comment: 49 pages; v2: minor improvements, references adde

Higgs branch localization in three dimensions

We show that the supersymmetric partition function of three-dimensional N =2 R-symmetric Chern-Simons-matter theories on the squashed S 3 and on S 2 7 S 1 can be computed with the so-called Higgs branch localization method, alternative to the more standard Coulomb branch localization. For theories that could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is dominated by BPS vortex strings sitting at two circles in the geometry. In this way, the partition function directly takes the form of a sum, over a finite number of points on the classical Coulomb branch, of a vortex-string times an antivortex-string partition functions. \ua9 2014 The Author(s)