Related papers: Classical Integrable Systems and Gauge Theory
Geometry of the solution space of the self-dual Yang-Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of…
In this work we compare different descriptions of the space of vacua of certain three dimensional N=4 superconformal field theories, compactified on a circle and mass-deformed to N=2 in a canonical way. The original N=4 theories are known…
In these lectures I will discuss the following topics: (1) Twistors in 4 flat dimensions: Massless particles; constrained phase space (x,p) versus twistors; Physical states in twistor space. (2) Introduction to 2T-physics and derivation of…
These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to…
We continue to investigate the relationship between the infrared physics of N=2 supersymmetric gauge theories in four dimensions and various integrable models such as Gaudin, Calogero-Moser and quantum spin chains. We prove interesting…
The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to…
We provide a concise approach to generalized dilaton theories with and without torsion and coupling to Yang-Mills fields. Transformations on the space of fields are used to trivialize the field equations locally. In this way their solution…
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
An intrinsically defined gauge-invariant discrete model of the Yang-Mills equations on a combinatorial analog of $\Bbb{R}^4$ is constructed. We develop several algebraic structures on the matrix-valued cochains (discrete forms) that are…
The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definition of noncommutative Yang-Mills theory: the continuum limit is approached at large $N$ by performing suitable double scaling limits, in which non-planar contributions…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are nonautonomous versions of the chiral model in (2+1) dimensions, generalized nonlinear…
In the case of a gauge-invariant discrete model of Yang-Mills theory difference self-dual and anti-self-dual equations are constructed.
We show that classical U(infinity) gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
A globally converging numerical method to solve coupled sets of non-linear integral equations is presented. Such systems occur e.g. in the study of Dyson-Schwinger equations of Yang-Mills theory and QCD. The method is based on the knowledge…