Related papers: Five dimensional gauge theories and vertex operato…
This is the 10th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It reviews correspondences between three-dimensional gauge theories and complex Chern-Simons theory on suitable…
We study a perturbation family of N=2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians. The 3d BPS half-index of the gauge theory…
We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional…
Five dimensional super conformal field theories can be studied using their geometric realisation as a limit of $M$-theory on a metrically conical Calabi-Yau threefold. We utilise this framework to investigate the phases of such theories…
We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic…
We determine the higher symmetries of 5d SCFTs engineered from M-theory on a $\mathbb{C}^3 / \Gamma$ background for $\Gamma$ a finite subgroup of $SU(3)$. This resolves a longstanding question as to how to extract this data when the…
We start a systematic study of quarter-BPS operators in four-dimensional $\mathcal{N}=4$ Super Yang-Mills with gauge group $\mathrm{SU}(N)$ making use of recently developed tools in conformal field theory. We adapt the technology of…
We consider 4d supersymmetric (special) unitary $\Gamma$ quiver gauge theories on compact manifolds which are $T^2$ fibrations over $S^2$. We show that their partition functions are correlators of vertex operators and screening charges of…
We construct actions for (p,0)- and (p,1)- supersymmetric, 1 <= p <= 4, two-dimensional gauge theories coupled to non-linear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We…
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge…
We study N=1 supersymmetric U(N) gauge theories coupled to an adjoint chiral field with superpotential. We consider the full supersymmetric moduli space of these theories obtained by adding all allowed chiral operators. These include…
Quantum toroidal algebras are obtained from quantum affine algebras by a further affinization, and, like the latter, can be used to construct integrable systems. These algebras also describe the symmetries of instanton partition functions…
We study the algebra of BPS Wilson loops in 3d gauge theories with N=2 supersymmetry and Chern-Simons terms. We argue that new relations appear on the quantum level, and that in many cases this makes the algebra finite-dimensional. We use…
Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual…
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions…
Based on any chiral vertex operator algebra satisfying a suitable finiteness condition, the semisimplicity of the zero-mode algebra as well as a regularity for induced modules, we construct conformal field theory over the projective line…
A connection between the gauge fixed dynamics of protected operators in superconformal Yang-Mills theory in four dimensions and Calogero systems is established. This connection generalizes the free Fermion description of the chiral primary…
Magnetic BPS string solutions preserving quarter of supersymmetry are obtained for all abelian gauged d=5 N=2 supergravity theories coupled to vector supermultiplets. Due to a ``generalised Dirac quantization'' condition satisfied by the…
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds…
We extend the study of BPS equations in ${\cal N}=1/2$ super Yang-Mills theory to the case of models with gauge symmetry breaking. We first consider an Abelian gauge-Higgs supersymmetric Lagrangian in $d=4$ dimensional Euclidean space…