Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group H4H_4

We show that the WZW model on the Heisenberg Lie group $H_4$ has Poisson-Lie symmetry only when the dual Lie group is ${ A}_2 \oplus 2{ A}_1$. In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group $H_4$ and its dual pair, ${ A}_2 \oplus 2{ A}_1$, as the target space in such a way that the original model is the same as the $H_4$ WZW model. Furthermore, we show that the dual model is conformal up to two loops order. Finally, we discuss $D$-branes and the worldsheet boundary conditions defined by a gluing matrix on the $H_4$ WZW model. Using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality transformations for the gluing matrix which locally defines the properties of the $D$-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group $H_4$ and its dual model.Comment: 17 page

(2+1)-dimensional interacting model of two massless spin-2 fields as a bi-gravity model

We propose a new group-theoretical (Chern-Simons) formulation for the bi-metric theory of gravity in (2+1)-dimensional spacetime which describe two interacting massless spin-2 fields. Our model has been formulated in terms of two dreibeins rather than two metrics. We obtain our Chern-Simons gravity model by gauging {\it mixed AdS-AdS Lie algebra} and show that it has a two dimensional conformal field theory (CFT) at the boundary of the anti de Sitter (AdS) solution. We show that the central charge of the dual CFT is proportional to the mass of the AdS solution. We also study cosmological implications of our massless bi-gravity model.Comment: 8 page

(1+1)-dimensional gauge symmetric gravity model and related exact black hole and cosmological solutions in string theory

We introduce a four-dimensional extension of the Poincar\'{e} algebra $(\mathcal{N})$ in (1+1)-dimensional space-time and obtain a (1+1)-dimensional gauge symmetric gravity model using the algebra $\mathcal{N}$. We show that the obtained gravity model is dual (canonically transformed) to the (1+1)-dimensional anti de Sitter ($AdS$) gravity. We also obtain some black hole and Friedmann-Robertson-Walker (FRW) solutions by solving its classical equations of motion. Then, we study $\frac{\mathbf{A}_{\mathbf{4,8}}}{\mathbf{A}_{\mathbf{1}}\otimes \mathbf{A}_{\mathbf{1}}}$ gauged Wess-Zumino-Witten (WZW) model and obtain some exact black hole and cosmological solutions in string theory. We show that some obtained black hole and cosmological metrics in string theory are same as the metrics obtained in solutions of our gauge symmetric gravity model.Comment: 15 pages. Section 4 is rewritten and 2 refs. are adde

Exact three dimensional black hole with gauge fields in string theory

We have obtained exact three dimensional BTZ type solutions with gauge fields, for string theory on a gauge symmetric gravitational background constructed from semi-simple extension of the Poincare algebra (and the Maxwell algebra) in 2 + 1 dimensions. We have studied the models for two non-Abelian and Abelian gauge fields solutions and shown that the related sigma models for each of these backgrounds is a SL(2;R) WZW (Wess-Zumino-Witten) model and that they are classically canonically equivalent. We have also obtained the dual solution for the Abelian case and by interpreting the new field strength tensors of the Abelian solution as electromagnetic field strength tensors shown that dual models coincide with the charged black string solution.Comment: 11 pages. Appendix and two references are adde

New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory

We construct black hole solutions to the leading order of string effective action in five dimensions with the source given by dilaton and magnetically charged antisymmetric gauge $B$-field. Presence of the considered $B$-field leads to the unusual asymptotic behavior of solutions which are neither asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional space part to correspond to the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston geometries of $E^3$, $S^3$, $H^3$, $H^2 \times E^1$, $\widetilde{{SL_2R}}$, nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature, entropy, dilaton charge, and magnetic potential, we show that the first law of black hole thermodynamics is satisfied by these quantities and the dilaton hair is of the secondary type. Furthermore, for Bianchi type $V$, the $T$-dual black hole solution is obtained which carries no charge associated with $B$-field and possesses a dilaton hair of secondary kind. Also, the entropy turns to be invariant under the $T$-duality