相关论文: Cluster Algebras and Supersymmetric Gauge Theories

We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.

We discuss the gauge natural formulation of supersymmetric theories and supergravity, with the aim to show that the standard and the supersymmetric frameworks admit in fact a unifying mathematical language.

$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the…

Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…

We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…

Seiberg-like duality of three dimensional N=2 Chern-Simons-Matter quiver gauge theory is shown to have a chiral double tropical cluster algebra structure. We use cluster algebra results to study combinatorial aspects of these theories such…

We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.

In the present paper we examine the relationship between several type $A$ cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes cluster algebras from surfaces, and encode several existing…

We interpret certain Seiberg-like dualities of two-dimensional N=(2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the…

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…

We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings.…

Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…

It is shown that N=2 supersymmetric theories with central charges present some hidden quartic symmetry. This enables us to construct representations of the quartic structure induced by superalgebra representations.

We classify all possible four-dimensional N=2 supersymmetric UV-complete gauge theories composed of semi-simple gauge groups and hypermultiplets. We also give appropriate references for all theories with known Seiberg-Witten solutions.

I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances.…

In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to…

Maximally supersymmetric gauge theories have experienced renewed interest due to the AdS/CFT correspondence and its conjectured S-duality. These gauge theories possess a large amount of symmetry and have quasi-integrable properties. We…

We clarify the natural cluster algebra of type A that exists in a residual and tropical form in the kinematical space as suggested in 1711.09102 by the use of triangulations, mutations and associahedron on the definition of scattering…