46 research outputs found
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
and type-I quantum superalgebras such as and are
known to admit non-trivial one-parameter families of infinite-dimensional and
finite dimensional irreps, respectively, even for generic . We develop a
technique for constructing the corresponding spectral-dependent R-matrices. As
examples we work out the the -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