Ali Eghbali

• 00
• 00 at Azarbaijan Shahid Madani University

By calculating inequivalent classical r-matrices for the $$gl(2,{\mathbb {R}})$$ g l ( 2 , R ) Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $$GL(2,{\mathbb {R}})$$ G L ( 2 , R ) Lie group in twelve inequivalent families. Most importantly, it...

By calculating inequivalent classical r-matrices for the $gl(2,\mathbb{R})$ Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE)), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $GL(2,\mathbb{R})$ Lie group in eleven inequivalent families. Most importantly, it is shown that each of these models c...

We proceed to generalize the Yang-Baxter (YB) deformation of Wess-Zumino-Witten (WZW) model to the Lie supergroups case. This generalization enables us to utilize various kinds of solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) to classify the YB deformations of WZW models based on the Lie supergroups. We obtain the ine...

The RKKY interaction between two impurities on a curved surface is investigated. Practical curved sample parameters are considered for investigating curvatures, similar to those observed experimentally in available samples such as graphene. For this type of two-dimensional curved systems and for two types of Schr\"{o}dinger and Dirac carriers, the...

We proceed to generalize the Yang-Baxter (YB) deformation of Wess-Zumino-Witten (WZW) model to the Lie supergroups case. This generalization enables us to utilize various kinds of solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) to classify the YB deformations of WZW models based on the Lie supergroups. We obtain the ine...

The RKKY interaction between two impurities on a curved surface is investigated. Practical curved sample parameters are considered for investigating curvatures, similar to those observed experimentally in available samples such as graphene. For this type of two-dimensional curved system and for two types of Schrödinger and Dirac carriers, the RKKY...

We proceed to investigate the non-Abelian T-duality of $$AdS_{2}$$ A d S 2 , $$AdS_{2}\times S^1$$ A d S 2 × S 1 and $$AdS_{3}$$ A d S 3 physical backgrounds, as well as the metric of the analytic continuation of $$AdS_{2}$$ A d S 2 from the point of view of Poisson-Lie (PL) T-duality. To this end, we reconstruct these metrics of the AdS families a...

We proceed to investigate the non-Abelian T-duality of $AdS_{2}$, $AdS_{2}\times S^1$ and $AdS_{3}$ physical backgrounds, as well as two-sphere $S^2$ from the point of view of Poisson-Lie (PL) T-duality. To this end, we reconstruct these metrics of the $AdS$ families as backgrounds of non-linear $\sigma$-models on two- and three-dimensional Lie gro...

The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group (H4) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the h4 Lie algebra by using its corresponding automorphism transformation. Then we show that YB deformations of H4 WZW model ar...

The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group ($H_4$) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the $ h_4$ Lie algebra by using its corresponding automorphism transformation. Then we show that YB deformations of $H_4$ WZ...

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $$\alpha '$$ α ′ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abe...

We generalize the formulation of Poisson-Lie (PL) T-plurality proposed by R. von Unge (2002) [6] from Lie groups to Lie supergroups. By taking a convenient ansatz for metric of the σ-model in terms of the left-invariant one-forms of the isometry Lie supergroups (C3+A) and GL(1|1) we construct cosmological string backgrounds, including (2+1|2)-dimen...

We generalize the formulation of Poisson-Lie (PL) T-plurality proposed by R. von Unge [JHEP 07 (2002) 014] from Lie groups to Lie supergroups. By taking a convenient ansatz for metric of the $\sigma$-model in terms of the left-invariant one-forms of the isometry Lie supergroups $(C^3 +A)$ and $GL(1|1)$ we construct cosmological string backgrounds,...

Using the homogeneous G\"{o}del spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $\alpha'$ including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of G\"{o}del string cosmologies via Poisson-Lie (PL) T-duality approach. In studying Abelia...

Exact conformal field theories (CFTs) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual σ-models (here as the PL T-duality on a semi-Abelian double) on 2+2-dimensional target manifolds M≈O×G and M˜≈O×G˜, where G and G˜ as two-dimensional real non-Abelian a...

Exact conformal field theories (CFTs) are obtained by using the approach of Poisson-Lie (PL) T-duality in the presence of spectators. We explicitly construct some non-Abelian T-dual $\sigma$-models (here as the PL T-duality on a semi-Abelian double) on $2+2$-dimensional target manifolds $M \approx O \times \bf G$ and ${\tilde M} \approx O \times {\...

According to the perturbation order, the equations of motion of low-energy string effective action are the generalized Einstein equations. Thus, by making use of the conformal transformation of the metric tensor, it is possible to map the low-energy string effective action into f(T) gravity, relating the dilaton field to the torsion scalar. Conside...

The non-Abelian T-dualization of the BTZ black hole is discussed in detail by using the Poisson-Lie T-duality in the presence of spectators. We construct explicitly a dual pair of sigma models related by Poisson-Lie symmetry. The original model is built on a $2+1$-dimensional manifold $M \approx O \times \bf G$, where $\bf G$ as a two-dimensional r...

The non-Abelian T-dualization of the BTZ black hole is discussed in detail by using the Poisson-Lie T-duality in the presence of spectators. We explicitly construct a dual pair of sigma models related by Poisson-Lie symmetry. The original model is built on a $2+1$-dimensional manifold ${\cal M} \approx O \times \bf G$, where $\bf G$ as a two-dimens...

Admissible structure constants related to the dual Lie superalgebras of particular Lie superalgebra $({\cal C}^3 + {\cal A})$ are found by a straightforward calculations from the matrix form of super Jacobi and mixed super Jacobi identities which are obtained form adjoint representation. Then, by making use of the automorphism supergroup of the Lie...

Admissible structure constants related to the dual Lie superalgebras of particular Lie superalgebra $({\cal C}^3 + {\cal A})$ are found by straightforward calculations from the matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation. Then, by making use of the automorphism supergroup of the Lie s...

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...

We consider cosmology of brane-world scenario in the frame work of teleparallel gravity in that way matter is localized on the brane. We show that the cosmology of such branes is different from the standard cosmology in teleparallelism. In particular, we obtain a class of new solutions with a constant five-dimensional radius and cosmologically evol...

The equations of motion of a super non-Abelian T-dual sigma model on the Lie supergroup $(C^1_1+A)$ in the curved background are explicitly solved in this contribution. In this way to find the solution of the flat model we use the transformation of supercoordinates transforming the metric into constant which we show it to be a supercanonical transf...

A WZW model on the Lie supergroup (C 3 + A) is constructed. It is shown that this model contains super Poisson-Lie symmetry with the dual Lie supergroup C 3 ⊕ A 1,1|.i. Furthermore, we show that the dual model is also equivalent to the WZW model on isomorphic Lie supergroup (C 3 + A).i. In this manner, because of isomorphism of the \( \left( {{{\ma...

We show that the WZNW model on the Lie supergroup GL(1|1) has super Poisson-Lie symmetry with the dual Lie supergroup B + A + A1;1|.i. Then, we discuss about D-branes and worldsheet boundary conditions on supermanifolds, in general, and obtain the algebraic relations on the gluing supermatrix for the Lie supergroup case. Finally, using the supercan...

We obtain the classical r-matrices of two and three dimensional Lie super-bialgebras. We thus classify all two and three dimensional coboundary Lie super-bialgebras and their types (triangular, quasi-triangular, or factorable). Using the Sklyanin superbracket, we then obtain the super Poisson structures on the related Poisson-Lie supergroups.

By direct calculations of matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation, and using the automorphism supergroup of the gl(1|1) Lie superalgebra, we determine and classify all gl(1|1) Lie superbialgebras. Then, by calculating their classical r-matrices, the gl(1j1) coboundary Lie superbia...

We generalize the formulation of Poisson-Lie T-dual sigma models on manifolds to supermanifolds. In this respect, we formulate 1+1 dimensional string cosmological models on the Lie supergroup C^3 and its dual (A_1,1 + 2A)^0_(1,0,0), which are coupled to two fermionic fields. Then, we solve the equations of motion of the models and show that there i...

Using adjoint representation we first classify two and three dimensional Lie superbialgebras obtained from decomposable Lie superalgebras. In this way we complete the classification obtained by Eghbali et al., [J. Math. Phys. 51, 073503 (2010); e-print arXiv:0901.4471 [math-ph]] . Then we classify all four and six dimensional Drinfel’d superdoubl...

Using adjoint representation of Lie superalgebras, we obtain the matrix form of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By direct calculations of these identities, and use of automorphism supergroups of two and three dimensional Lie superalgebras, we obtain and classify all two and three dimensional Lie superbialgebra...

We investigate Poisson-Lie symmetry for T-dual sigma models on supermanifolds in general and on Lie supergroups in particular. We show that the integrability condition on this super Poisson-Lie symmetry is equivalent to the super Jacobi identities of the Lie super-bialgebras. As examples we consider models related to four dimensional Lie super-bial...