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We study the deep connection between integrable models and Poisson-Lie T-duality working on a finite dimensional example constructed on SL(2,C) and its Iwasawa factors SU(2) and B. We shown the way in which Adler-Kostant-Symes theory and…
We discuss two classes of exact (in $\a'$) string solutions described by conformal sigma models. They can be viewed as two possibilities of constructing a conformal model out of the non-conformal one based on the metric of a $D$-dimensional…
The complete solution of the vacuum Kerr-Schild equations in general relativity is presented, including the space-times with a curved background metric. The corresponding result for a flat background has been obtained by Kerr.
The symmetry properties of the bosonic string effective action under Poisson-Lie duality transformations are investigated. A convenient and simple formulation of these duality transformations is found, that allows the reduction of the…
Covariance of the one-loop renormalization group equations with respect to Poisson-Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson-Lie sigma models with truncated matrices…
For Green-Schwarz superstring sigma-model on curved backgrounds, we introduce a non-metric measure $\Phi \equiv \epsilon^{i j} \epsilon^{I J} (\partial_i \varphi^I) (\partial_j \varphi^J)$ with two scalars $\varphi^I (I = 1, 2)$ used in Two…
Poisson-Lie T-plurality constructs a chain of supergravity solutions from a Poisson-Lie symmetric solution. We study the Poisson-Lie T-plurality for supergravity solutions with $H$-flux, which are not Poisson-Lie symmetric but admit…
Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the…
We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an effective theory of the 3d Courant Sigma Model associated to the double of the underlying Lie bialgebroid. This field-theoretic result follows from a Lie-theoretic…
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by…
We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional…
The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…
Using the loop variable formalism as applied to a sigma model in curved target space, we give a systematic method for writing down gauge and generally covariant equations of motion for the modes of the free open string in curved space. The…
The description of the two sets of (4,0) supersymmetric models that are related by non-abelian duality transformations is given. The (4,0) supersymmetric WZNW is constructed and the formulation of the (4,0) supersymmetric sigma model dual…
Let G be a n-dimensional Lie group (n>2) with a bi-invariant Riemannian metric. We prove that if a surface of constant Gaussian curvature in G can be expressed as the product of two curves, then it must be flat. In particular, we can…
We find the explicit T-duality transformation in the phase space formulation of the N=(1,1) sigma model. We also show that the T-duality transformation is a symplectomorphism and it is an element of O(d,d). Further, we find the explicit…
The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates…
We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian "correspondence" space,…
The account of the Poisson-Lie T-duality is presented for the case when the action of the duality group on a target is not free. At the same time a generalization of the picture is given when the duality group does not even act on…
We carry out a Hamiltonian analysis of Poisson-Lie T-duality based on the loop geometry of the underlying phases spaces of the dual sigma and WZW models. Duality is fully characterized by the existence of equivariant momentum maps on the…