Related papers: Integrable sigma models on Riemann surfaces
We discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a…
Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…
Wave maps (i.e. nonlinear sigma models) with torsion are considered in 2+1 dimensions. Global existence of smooth solutions to the Cauchy problem is proven for certain reductions under a translation group action: invariant wave maps into…
We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general…
We show that a conformal connection on a closed oriented surface $\Sigma$ of negative Euler characteristic preserves precisely one conformal structure and is furthermore uniquely determined by its unparametrised geodesics. As a corollary it…
We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an involution $\sigma$ of $G$. The Poisson brackets and the classical local conserved…
Duality groups as (spontaneously broken) gauge symmetries for toroidal backgrounds, and their role in ($\infty$-dimensional) underlying string gauge algebras are reviewed. For curved backgrounds, it is shown that there is a duality in the…
Nonlinear sigma models arise in supergravity theories with or without matter couplings in various dimensions and they are important in understanding the duality symmetries of M-theory. With this motivation in mind, we review the salient…
This paper discusses a procedure for the consistent coupling of gauge- and matter superfields to supersymmetric sigma-models on symmetric coset spaces of Kaehler type. We exhibit the finite isometry transformations and the corresponding…
It is shown that a large class of systems of non-linear wave equations, based on the good-bad-ugly model, admit formal solutions with polyhomogeneous expansions near null infinity. A particular set of variables is introduced which allows us…
The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We endow the surface with a useful Riemannian metric which is…
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical…
We show that flag manifold $\sigma$-models (including $\mathbb{CP}^{n-1}$, Grassmannian models as special cases) and their deformed versions may be cast in the form of gauged bosonic Thirring/Gross-Neveu-type systems. Quantum mechanically…
A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of dimension equal to the number of degrees of…
In this paper we consider determining a minimal surface embedded in a Riemannian manifold $\Sigma\times \mathbb{R}$. We show that if $\Sigma$ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated…
We introduce non-linear $\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point space and the circle and illustrate some…
Several simple asymptotically-free chiral gauge theories are studied. The only ``free parameters'' of our models are the choice of the gauge group and the matter Weyl fermion representations, and the relative magnitudes of the…
Supersymmetric nonlinear sigma models are obtained from linear sigma models by imposing supersymmetric constraints. If we introduce auxiliary chiral and vector superfields, these constraints can be expressed by D-terms and F-terms depending…
We study non-linear $\sigma$-models defined on noncommutative torus as a two dimensional string world-sheet. We consider a quantum group as a noncommutative space-time as well as two points, a circle, and a noncommutative torus. Using the…