Related papers: Classical Integrability of Two Dimensional Non Lin…
We formulate four-dimensional N=2 supersymmetric nonlinear sigma models in N=1 superspace. We show how to add superpotentials consistent with N=2 supersymmetry. We lift our construction to higher-dimensional spacetime and write…
We study the noncommutative extensions of certain integrable field theories, namely the sine- and sinh-Gordon (sG and shG) models, and the U(N) principal chiral model (pcm). We argue that the Moyal deformations of the sG and shG models are…
The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The…
We summarize some (mostly geometric) facts underlying the relation between 2D integrable sigma models and generalized Gross-Neveu models, emphasizing connections to the theory of nilpotent orbits, Springer resolutions and quiver varieties.…
We derive conditions for $L_2$ differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions…
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
The complete integrability of a class of dynamical systems with the potential v(q)=q^{-2}+c q^2 is proved.
We investigate extremal metrics at which various types of rigidity theorems involving scalar curvatures hold. The rigidity we discuss here is related to the rigidity theorems presented by Mario Listing in his previous preprint. More…
We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.
In the study of integrable non-linear $\sigma$-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central role. For a large class of such…
We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential,…
We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two…
We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma…
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws is discussed. In the generic case, nonlocal conservation…
We consider several classes of $\sigma$-models (on groups and symmetric spaces, $\eta$-models, $\lambda$-models) with local couplings that may depend on the 2d coordinates, e.g. on time $\tau$. We observe that (i) starting with a…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in…
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
Using 4D, N=1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a…