arXiv subjects

C. Klimcik

Publications and source records attributed to C. Klimcik.

53 records · Page 3Linked to original sources

arXiv1995

Poisson-Lie T-duality: Open Strings and D-branes

Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold $G$ are dual to $D$-brane - anti-$D$-brane pairs propagating on the dual group manifold $\ti G$. The $D$-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group $\ti G$ by the dressing action of the group $G$. T-duality maps the momentum of the open string into the mutual distance of the $D$-branes in the pair. The whole picture is then extended to the full modular space $M(D)$ of the Poisson-Lie equivalent $\si$-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of $D$-branes living on targets belonging to $M(D)$. In this more general case the $D$-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.

hep-th↗

arXiv1995

Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles

A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of $σ$-models related by Poisson-Lie T-duality. Remarkably, the action contains a WZW-term on the Drinfeld double not only for conformally invariant $\si$-models. The resulting actions of the models from the dual pair differ just by a total derivative corresponding to an ambiguity in specifying a two-form whose exterior derivative is the WZW three-form. This total derivative is nothing but the Semenov-Tian-Shansky symplectic form on the Drinfeld double and it gives directly a generating function of the canonical transformation relating the $\si$-models from the dual pair.

hep-th↗

arXiv1995

Simple field theoretical models on noncommutative manifolds

We review recent progress in formulating two-dimensional models over noncommutative manifolds where the space-time coordinates enter in the formalism as non-commuting matrices. We describe the Fuzzy sphere and a way to approximate topological nontrivial configurations using matrix models. We obtain an ultraviolet cut off procedure, which respects the symmetries of the model. The treatment of spinors results from a supersymmetric formulation; our cut off procedure preserves even the supersymmetry.

hep-th↗

arXiv1995

Topologically nontrivial field configurations in noncommutative geometry

In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only finite number of modes.

hep-th↗

arXiv1995

Quantum Poisson-Lie T-duality and WZNW model

A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.

hep-th↗

arXiv1995

Field Theory on a Supersymmetric Lattice

A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integer-valued sequence of finite dimensional rings of supermatrices and by using the differencial calculus of non-commutative geometry. The regulated theory involves only finite number of degrees of freedom and is manifestly supersymmetric.

hep-th↗

arXiv1995

Dual Non-Abelian Duality and the Drinfeld Double

The standard notion of the non-Abelian duality in string theory is generalized to the class of $\si$-models admitting `non-commutative conserved charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg ,\cgt)$ and they possess an isometry group iff the commutant $[\cgt,\cgt]$ is not equal to $\cgt$. Within the enlarged class of the backgrounds the non-Abelian duality {\it is} a duality transformation in the proper sense of the word. It exchanges the roles of $\cg$ and $\cgt$ and it can be interpreted as a symplectomorphism of the phase spaces of the mutually dual theories. We give explicit formulas for the non-Abelian duality transformation for any $(\cg,\cgt)$. The non-Abelian analogue of the Abelian modular space $O(d,d;{\bf Z})$ consists of all maximally isotropic decompositions of the corresponding Drinfeld double.

hep-th↗

arXiv1995

Towards Finite Quantum Field Theory in Non-Commutative Geometry

We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect to the isometries of the sphere. We explicitely show that the model is finite and the UV-regularization automatically takes place.

hep-th↗

arXiv1995

`Null gauged' WZNW theories and Toda-like $σ$-models

A new method of gauging of WZNW models is presented, leading to a class of exact string solutions with a target space metric of Minkowskian signature. The corresponding models may be interpreted as $σ$-model analogues of the Toda field theories.

hep-th↗

arXiv1994

Strings in Spacetime Cotangent Bundle and T-duality

A simple geometric description of T-duality is given by identifying the cotangent bundles of the original and the dual manifold. Strings propagate naturally in the cotangent bundle and the original and the dual string phase spaces are obtained by different projections. Buscher's transformation follows readily and it is literally projective. As an application of the formalism, we prove that the duality is a symplectomorphism of the string phase spaces.

hep-th↗

arXiv1994

Non-commutative black holes in $D$ dimensions

Recently introduced classical theory of gravity in non-commutative geometry is studied. The most general (four parametric) family of $D$ dibensional static spherically symmetric spacetimes is identified and its properties are studied in detail. For wide class of the choices of parameters, the corresponding spacetimes have the structure of asymptotically flat black holes with a smooth event horizon hiding the curvature singularity. A specific attention is devoted to the behavior of components of the metric in non-commutative direction, which are interpreted as the black hole hair.

gr-qc↗

arXiv1994

Exact four dimensional string solutions and Toda-like sigma models from `null-gauged' WZNW theories

We construct a new class of exact string solutions with a four dimensional target space metric of signature ($-,+,+,+$) by gauging the independent left and right nilpotent subgroups with `null' generators of WZNW models for rank 2 non-compact groups $G$. The `null' property of the generators (${\rm Tr }(N_n N_m)=0$) implies the consistency of the gauging and the absence of $\a'$-corrections to the semiclassical backgrounds obtained from the gauged WZNW models. In the case of the maximally non-compact groups ($G= SL(3), SO(2,2), SO(2,3), G_2$) the construction corresponds to gauging some of the subgroups generated by the nilpotent `step' operators in the Gauss decomposition. The rank 2 case is a particular example of a general construction leading to conformal backgrounds with one time-like direction. The conformal theories obtained by integrating out the gauge field can be considered as sigma model analogs of Toda models (their classical equations of motion are equivalent to Toda model equations). The procedure of `null gauging' applies also to other non-compact groups.

hep-th↗

arXiv1993

Duality invariant class of exact string backgrounds

We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.

hep-th↗

arXiv1993

Black Hole with Non-Commutative Hair

The specific nonlinear vector $σ$-model coupled to Einstein gravity is investigated. The model arises in the studies of the gravitating matter in non-commutative geometry. The static spherically symmetric spacetimes are identified by direct solving of the field equations. The asymptotically flat black hole with the ``non-commutative'' vector hair appears for the special choice of the integration constants, giving thus another counterexample to the famous ``no-hair'' theorem.

gr-qc↗

arXiv1993

Grading of Spinor Bundles and Gravitating Matter in Non-Commutative Geometry

The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields coupled to the standard Einstein gravity.The matter multiplet is encoded in the Dirac operator which yields the representation of the algebra of the universal forms. The general form of the Dirac operator depends on a choice of the grading of the corresponding spinor bundle. A choice is given, which leads to the nonlinear vector sigma-model coupled to the Einstein gravity.

hep-th↗

arXiv1993

Quantum Fluctuations and Curvature Singularities in Jackiw-Teitelboim Gravity

The Jackiw-Teitelboim gravity with the matter degrees of freedom is considered. The classical model is exactly solvable and its solutions describe non-trivial gravitational scattering of matter wave-packets. For huge amount of the solutions the scattering space-times are free of curvature singularities. However, the quantum corrections to the field equations inevitably cause the formation of (thunderbolt) curvature singularities, vanishing only in the limit $\hbar\to 0$. The singularities cut the space-time and disallow propagation to the future.The model is inspired by the dimensional reduction of 4-d pure Einstein gravity, restricted to the space-times with two commuting space-like Killing vectors. The matter degrees of freedom also stem from the 4-d ansatz. The measures for the continual integrations are judiciously chosen and one loop contributions (including the graviton and the dilaton ones) are evaluated. For the number of the matter fields $N=24$ we obtain even the exact effective action, applying the DDK-procedure. The effective action is nonlocal, but the semiclassical equations can be solved by using some theory of the Hankel transformations.

hep-th↗

arXiv1992

Grassmann Integral Topological Invariants

Partition functions of some two-dimensional statistical models can be represented by means of Grassmann integrals over loops living on two-dimensional torus. It is shown that those Grassmann integrals are topological invariants, which depend only on the winding numbers of the loops. The fact makes possible to evaluate the partition functions of the models and the statistical mean values of certain topological characteristics (indices) of the configurations, which behave as the (topological) order parameters.

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