Classical solutions of sigma models in curved backgrounds by the Poisson-Lie T-plurality

Classical equations of motion for three-dimensional sigma-models in curved background are solved by a transformation that follows from the Poisson-Lie T-plurality and transform them into the equations in the flat background. Transformations of coordinates that make the metric constant are found and used for solving the flat model. The Poisson-Lie transformation is explicitly performed by solving the PDE's for auxiliary functions and finding the relevant transformation of coordinates in the Drinfel'd double. String conditions for the solutions are preserved by the Poisson-Lie transformations. Therefore we are able to specify the type of sigma-model solutions that solve also equations of motion of three dimensional relativistic strings in the curved backgrounds. Simple examples are given

Flat coordinates and dilaton fields for three--dimensional conformal sigma models

Riemannian coordinates for flat metrics corresponding to three--dimensional conformal Poisson--Lie T--dualizable sigma models are found by solving partial differential equations that follow from the transformations of the connection components. They are then used for finding general forms of the dilaton fields satisfying the vanishing beta equations of the sigma models.Comment: 16 pages, no figure

Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing beta-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to various decompositions of Drinfeld double. Models with nontrivial dilaton field may appear. It turns out that for ``traceless'' dual algebras they satisfy the vanishing beta-function equations as well. In certain cases the dilaton cannot be defined in some of the dual models. We provide an explanation why this happens and give criteria predicting when it happens.Comment: 24 pages, the published version; changes compared to v1: typos corrected, conclusions extended, added reference

Algebraic Framework for Quantization of Nonultralocal Models

Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang--Baxter--type consistency conditions as well as conditions for the existence of the multiple coproduct (monodromy matrix), which can be used for construction of the commuting subalgebra, are given. Homogeneous and local algebras are introduced, and simplification of the Yang--Baxter--type conditions for them is shown. The Yang--Baxter--type equations and multiple coproduct conditions for homogeneous and local of order 2 algebras are solved.Comment: 18 pages, Latex, one formula plus two citations added, several misprints were correcte

On the nonsymmetric purely affine gravity

We review the vacuum purely affine gravity with the nonsymmetric connection and metric. We also examine dynamical effects of the second Ricci tensor and covariant second-rank tensors constructed from the torsion tensor in the gravitational Lagrangian.Comment: 15 pages; published versio

Utilization of diffraction analysis in the study of martensitic weld deposits using tungsten carbide particles on S235JR+N steel

The durability of classic structural steels against various types of wear is generally low. Therefore, various types and combinations of resilient materials are constantly evolving, which are designed to reduce the cost of components replacement or repairs. This paper deals with the structures that are formed in a weld after addition of tungsten carbide particles to protect the surface of the components from wear. The resistance of the weld surface layer containing tungsten carbides is also evaluated in comparison with a layer without these particles

On modular spaces of semisimple Drinfeld doubles

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different from the known one for Abelian Drinfeld double, since some of these Drinfeld doubles allow decomposition into several non-isomorphic Manin triples and their modular spaces are therefore written as unions of homogeneous spaces of different dimension. Implications for Poisson-Lie T-duality and especially Poisson-Lie T-plurality are mentioned.Comment: 15 pages; introduction enlarged, added reference

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

Worldsheet boundary conditions in Poisson-Lie T-duality

We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in two non-Abelian Drinfel'd doubles.Comment: 20 pages, Latex; v2: typos and wording corrected, references added; v3: three-dimensional example added, reference added, discussion clarified, published versio