Quiver

About: Quiver is a research topic. Over the lifetime, 4504 publications have been published within this topic receiving 94875 citations.

N=2 dualities

Abstract: We study the generalization of S-duality and Argyres-Seiberg duality for a large class of N = 2 superconformal gauge theories. We identify a family of strongly interacting SCFTs and use them as building blocks for generalized superconformal quiver gauge theories. This setup provides a detailed description of the “very strongly coupled” regions in the moduli space of more familiar gauge theories. As a byproduct, we provide a purely four dimensional construction of N = 2 theories defined by wrapping M5 branes over a Riemann surface.

Renormalization group flows from holography supersymmetry and a c theorem

Abstract: We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 super-Yang-Mills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N = 4 gauged supergravity theory holographically dual to a sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For evendimensional boundaries, the c-function coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.

Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras

Abstract: To Professor Shoshichi Kobayashi on his 60th birthday 1. Introduction. In this paper we shall introduce a new family of varieties, which we call quiver varieties, and study their geometric structures. They have close relation to the singularity theory and the representation theory of the Kac-Moody algebras. Our original motivation was to study solutions of the anti-self-dual Yang-Mills equations on a particular class of 4-dimensional noncompact complete manifolds, the so-called ALE spaces (or the ALE gravitational instantons), which were constructed by Kronheimer [Krl]. In [KN] we gave a description of the framed moduli space of all solutions in terms of solutions of a system of quadratic equations (called the ADHM equations) for representations of a quiver on an affine, simply laced Dynkin graph. It is an analogue of the description, given by Atiyah, Drinfeld, Hitchin, and Manin [ADHM], of the moduli space for IR 4 (or S4) in terms of solutions of a quadratic equation for certain finite-dimensional matrices. Once we set aside their gauge-theoretic origin, there is no longer reason to restrict ourselves to affine Dynkin graphs. Definitions can be generalized to arbitrary finite graphs. We get what we call quiver varieties. We study geometric structures of quiver varieties in this paper. In [Nal] it was noticed that the moduli space of anti-self-dual connections on ALE spaces has a hyper-K/ihler structure, namely a Riemannian metric equipped with three endo-morphisms I, J, K of the tangent bundle which satisfy the relations of quaternion algebra and are covariant constant with respect to the Levi-Civita connection: The same holds for general quiver varieties. In particular, quiver varieties have holomorphic symplectic forms. We study further properties of the quiver variety, such as a natural *-action, symplectic geometry, topology, and so on. As ALE spaces closely related to simple singularities, quiver varieties have very special kinds of singularities that enjoy very nice properties. Surprisingly, the ADHM equation appears in a very different context. In [L3] Lusztig used it to construct \"canonical bases\" of the part U-of the quantized enveloping algebra U associated by Drinfeld and Jimbo to the graph. Motivated by his results, we give a geometric construction of irreducible highest-weight integrable representations of the Kac-Moody algebra associated to the graph (Theorem 10.14). The weight space of the representation space will be given as a vector space consisting of constructible functions on a Lagrangian subvariety of a quiver variety. The action of the Kac-Moody …

A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories

Abstract: We propose a relation between correlation functions in the 2d A(N-1) conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers [1]. New features appear in the analysis that have no counterparts in the Liouville case.

A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories

Abstract: We propose a relation between correlation functions in the 2d A_{N-1} conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N=2 SU(N) 4d quiver gauge theories. Our proposal generalises the recently uncovered relation between the Liouville theory and SU(2) quivers. New features appear in the analysis that have no counterparts in the Liouville case.