arXiv subjects

Ali Eghbali

Publications and source records attributed to Ali Eghbali.

At least 19 recordsLinked to original sources

arXiv2026

D-branes in $AdS_2 \times H^2 \times H^2$ under the non-Abelian T-duality

We proceed to construct a non-Abelian dual pair for the $AdS_2 \times H^2 \times H^2$ background by applying the non-Abelian T-duality (here as Poisson-Lie T-duality on a semi-Abelian double). By using a certain parameterization of the $6$-dimensional Lie group ${A}_2 \otimes {A}_2 \otimes A_2$ we construct the original $\sigma$-model including the $AdS_2 \times H^2 \times H^2$ metric in the absence of $B$-field. It is shown that the dual background constructed by means of the Poisson-Lie T-duality is supported by a $B$-field and a metric whose contains a physical singularity. By studying the behavior of the dual spacetime at small $(r , y, u)$ coordinates, we show that the dual metric with a zero field strength and a non-trivial dilaton field make up a solution for the vanishing of the one-loop beta-function equations. Furthermore, at large $(r , y, u)$, it is shown that the $AdS_2 \times H^2 \times H^2$ solution is preserved under the non-Abelian T-duality. Finally, using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality for the gluing matrix which locally defines the properties of the D-brane, we find seven different cases of the gluing matrices for the $AdS_2 \times H^2 \times H^2$ $\sigma$-model and its dual pair. In this way, it is found a symmetric duality action on the branes linking together in a duality chain.

hep-th↗

arXiv2026

Integrable sigma models with Haantjes structure on ${H_{4}}$ Lie group

By solving algebraic relations for the conditions of Haantjes structure on a Lie algebra ${\G}$ and by using the corresponding automorphism group we proceed to classify all inequivalent algebraic Haantjes structures on ${\G}$. In this manner, we obtain 34 inequivalent algebraic Haantjes structures on the ${h_{4}}$ Lie algebra. We deform the chiral sigma model on a Lie group by using Haantjes structure on it. Then we try to obtain conditions on this structure such that the deformed sigma model remains to be integrable. Finally, using the ${h_{4}}$ Haantjes structures and solving this conditions three new integrable sigma models on the ${H_{4}}$ Lie group are obtained.

hep-th↗

arXiv2025

Yang-Baxter deformations of the OSP(1|2) WZW model

We obtain inequivalent classical r-matrices of the $osp(1|2)$ Lie superalgebra as real solutions of the graded (modified) classical Yang-Baxter equation, in such a way that the corresponding automorphism transformation is employed. Then, Yang-Baxter deformations of the Wess-Zumino-Witten model based on the OSP$(1|2)$ Lie supergroup are specified by super skew-symmetric classical r-matrices. In this regard, the effect coming from the deformation is reflected as the coefficient of both metric and $B$-field. Furthermore, it is shown that all resulting classical r-matrices are non-Abelian and also non-unimodular, which leads us to graded generalized supergravity equations. We show that the background of undeformed model is a solution of the graded generalized supergravity equations when supplemented by an appropriate supervector field obtaining from the linear combination of the Killing supervectors corresponding to the background, while the deformed models do not satisfy these equations. This is consistent with our expectations, since the deformed models under consideration do not describe a Green-Schwarz superstring. However, the deformed backgrounds are interesting, in particular in the OSP$(1|2)$ case they are rare, much hard technical work was needed to obtain them.

hep-th↗

arXiv2025

More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations

In superdimension $(2|2)$ there are only three non-Abelian Lie superalgebras admitting non-degenerate ad-invariant supersymmetric metric, the well-known Lie superalgebra $gl(1|1)$, and two more, $({\C}^3 + \A)$ and $({\C}_0^5 +{\A})$. After a brief review of the construction of the Wess-Zumino-Witten (WZW) models based on the $GL(1|1)$ and $(C^3 + A)$ Lie supergroups, we proceed to construct the WZW model on the $({C}_0^5 +{A})$ Lie supergroup. Unfortunately, this model does not include the super Poisson-Lie symmetry. In the following, three new exact conformal field theories of the WZW type are constructed by gauging an anomaly-free subgroup SO(2) of the Lie supergroups mentioned above. The most interesting indication of this work is that the gauged WZW model on the supercoset $(C^3 + A)/$SO(2) has super Poisson-Lie symmetry; most importantly, its dual model is conformally invariant at the one-loop order, and this is presented here for the first time. Finally, in order to study the Yang-Baxter (YB) deformations of the $({C}_0^5 +{A})$ WZW model we obtain the inequivalent solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) for the $({\C}_0^5 +{\A})$ Lie superalgebra. Then, we classify all possible YB deformations for the $({C}_0^5 +{A})$ and settle also the issue of an one-loop conformality of the deformed backgrounds. The classification results are important, in particular in the Lie supergroup case they are rare, much hard technical work was needed to obtain them.

hep-th↗

arXiv2025

Non-Abelian target space duals of Thurston geometries

In this study, we proceed to investigate the Thurston geometries from the point of view of their Poisson-Lie (PL) T-dualizability. First of all, we find all subalgebras of Killing vectors that generate group of isometries acting freely and transitively on the three-dimensional target manifolds, where the Thurston metrics are defined. It is shown that three-dimensional Lie subalgebras are isomorphic to the Bianchi type algebras. We take the isometry subgroup of the metric as the first subgroup of Drinfeld double. In order to investigate the non-Abelian T-duality, the second subgroup must be chosen to be Abelian. Accordingly, the non-Abelian target space duals of these geometries are found via PL T-duality approach in the absence of $B$-field. We also comment on the conformal invariance conditions of the T-dual $σ$-models under consideration.

hep-th↗

arXiv2025

Integrable deformed H$_{_{4}}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations

We show that the Yang-Baxter (YB) deformed backgrounds of the Wess-Zumino-Witten (WZW) model based on the $H_{_{4}}$ Lie group can be considered as solutions of the generalized supergravity equations (GSEs). Then, by applying the Poisson-Lie T-duality in the presence of spectator fields, we obtain the non-Abelian target space duals of those models. It is shown that all dual models (except for one model) are integrable and most interestingly, they satisfy the GSEs. As a final remark, we show that all solutions of the GSEs for the original models are trivial.

hep-th↗

arXiv2024

Generalized Supergravity Equations for the WZW Model

Generalized supergravity equations (GSEs) were originally proposed as a modification of the standard IIB supergravity equations to satisfy the background of $η$-deformed $AdS_5 \times S^5$ introduced by Arutyunov {\it et al}. In this study, we proceed to write down the GSEs for the Wess-Zumino-Witten (WZW) models based on Lie groups. First, we simplify the GSEs for the WZW model by imposing the conditions for vanishing of the one-loop beta function equations. Then, by introducing an {\it Ansatz} for the Killing vector field $I$, it is shown that the Killing equation ${\cal L}_{_{I}} G_{_{μν}}=0$ is held. In addition, we introduce a generalized Killing vector such that the existence of a solution to the GSEs requires that this vector be light-like. In this way, we solve the simplified GSEs for the WZW models constructed on Lie groups up to dimension five. Unfortunately, two of the groups do not have light-like vectors and therefore do not admit the GSEs.

hep-th↗

arXiv2024

$AdS_3 \times S^3$ Background from Poisson-Lie T-Duality

We proceed to construct a dual pair for the $AdS_3 \times S^3$ background by applying non-Abelian T-duality (here as Poisson-Lie (PL) T-duality on a semi-Abelian double). By using a certain parametrization of the $4$-dimensional Lie group ${A}_2 \otimes 2{A}_1$ and by a suitable choice of spectator-dependent matrices, the original $σ$-model including the $AdS_3 \times S^3$ metric and a non-trivial $B$-field are constructed. The dual background constructed by means of the PL T-duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non-trivial $H$-flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non-Abelian T-dual $σ$-models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two-loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.

hep-th↗

arXiv2024

A hierarchy of WZW models related to super Poisson-Lie T-duality

Motivated by super Poisson-Lie (PL) symmetry of the Wess-Zumino-Witten (WZW) model based on the $(C^3+A)$ Lie supergroup of our previous work [A. Eghbali {\it et al.} JHEP 07 (2013) 134], we first obtain and classify all Drinfeld superdoubles (DSDs) generated by the Lie superbialgebra structures on the $({\cal C}^3+ {\cal A})$ Lie superalgebra as a theorem. Then, introducing a general formulation we find the conditions under which a two-dimensional $σ$-model may be equivalent to a WZW model. With the help of this formulation and starting the super PL symmetric $(C^3+A)$ WZW model, we get a hierarchy of WZW models related to super PL T-duality, in such a way that it is different from the super PL T-plurality, because the DSDs are, in this process, non-isomorphic. The most interesting indication of this work is that the $(C^3+A)$ WZW model does remain invariant under the super PL T-duality transformation, that is, the model is super PL self-dual.

hep-th↗

arXiv2024

T-duality/plurality of BTZ black hole metric coupled to two fermionic fields

We ask the question of classical super (non-)Abelian T-duality for BTZ black hole metric coupling to two fermionic fields. Our approach is based on super Poisson-Lie (PL) T-duality in the presence of spectator fields. In order to study the Abelian T-duality of the metric we dualize over the Abelian Lie supergroups of the types $(1|2)$ and $(2|2)$, in such a way that it is shown that both original and dual backgrounds of the models are conformally invariant up to one-loop order in the presence of field strength. Then, we study the non-Abelian T-duality of the BTZ vacuum metric coupling to two fermionic fields. The dualizing is performed on some non-Abelian Lie supergroups of the type $(2|2)$, in such a way that we are dealing with semi-Abelian superdoubles which are non-isomorphic as Lie superalgebras in each of the models. In the non-Abelian T-duality case, it is interesting to mention that the models can be conformally invariant up to one-loop order in both cases of the absence and presence of field strength. In addition, starting from the decomposition of semi-Abelian Drinfeld superdoubles generated by some of the ${\cal C}^3 \oplus {\cal A}_{1,1}$ Lie superbialgebras we study the super PL T-plurality of the BTZ vacuum metric coupled to two fermionic fields. However, our findings are interesting in themselves, but at a constructive level, can prompt many new insights into supergravity and manifestly have interesting mathematical relationships with double field theory.

hep-th↗

arXiv2024

Solutions of generalized supergravity equations with the BTZ black hole metric

We proceed to investigate the solutions of generalized supergravity equations (GSE) in three dimensions. Our candidate is the metric of BTZ black hole. It is shown that only the cases with $J=M=0$ and $J=0,~ M\neq 0$ of the BTZ metric satisfy the GSE. In the former, we find a family of solutions including the field strength $H_{_{r φt}}=2r/l$, the cosmological constant $Λ=-1/l^2$, one-form $Z_μ$ and a vector field which is obtained to be a linear combination of the directions of the time translation and rotational symmetries. In the latter, the solutions possess the same field strength as before, while the cosmological constant $Λ$, one-form $Z_μ$ and vector field $I$ will be different from the previous case. Finally, we show that the charged black string solution found by Horne and Horowitz, which is Abelian T-dual to the the BTZ black hole solution, can be considered as a solution for the GSE.

hep-th↗

arXiv2023

Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality

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 twelve inequivalent families. Most importantly, it is shown that each of these models can be obtained from a Poisson-Lie T-dual $σ$-model in the presence of the spectator fields when the dual Lie group is considered to be Abelian, i.e. all deformed models have Poisson-Lie symmetry just as undeformed WZW model on the $GL(2,\mathbb{R})$. In this way, all deformed models are specified via spectator-dependent background matrices. For one case, the dual background is clearly found.

hep-th↗

arXiv2023

Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3 +A)$

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 inequivalent solutions (classical r-matrices) of the (m)GCYBE for the $gl(1|1)$ and $({\cal C}^3 +{\cal A})$ Lie superalgebras in the non-standard basis, in such a way that the corresponding automorphism transformations are employed. Then, the YB deformations of the WZW models based on the $GL(1|1)$ and $(C^3 + A)$ Lie supergroups are specified by skew-supersymmetric classical r-matrices satisfying (m)GCYBE. In some cases for both families of deformed models, the metrics remain invariant under the deformation, while the components of $B$-fields are changed. After checking the conformal invariance of the models up to one-loop order, it is concluded that the $GL(1|1)$ and $(C^3 + A)$ WZW models are conformal theories within the classes of the YB deformations preserving the conformal invariance. However, our results are interesting in themselves, but at a constructive level, may prompt many new insights into (generalized) supergravity solutions.

hep-th↗

arXiv2023

RKKY interaction on curved surfaces: Different behavior of Dirac and Schrödinger carriers as interaction mediating particles

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 Schrödinger and Dirac carriers, the RKKY interaction and local density of states (LDOS) are calculated. Results show that the strength of the RKKY interaction on a curved surface depends significantly on the nature of particles embedded on this surface, indicating that the geometry has a different effect on the dynamics of Schrödinger and Dirac carriers. While the curved surface increases the RKKY interaction strength for Schrödinger-type carriers in comparison with the flat sample, RKKY interaction decreases in the curved surface for Dirac-type particles. This can be understood regrading the effective magnetic field experienced by the Dirac particles as a result of the curved surface. There is also a correlation between LDOS and the RKKY interaction, which could be explained by the effect of conducting electrons density on the exchange interaction mediated by these carriers.

cond-mat.mes-hall↗

arXiv2022

Non-Abelian T-duality of $AdS_{d\le3}$ families by Poisson-Lie T-duality

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 the metric of the analytic continuation of $AdS_{2}$ 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 $σ$-models on two- and three-dimensional Lie groups. By considering the Killing vectors of these metrics and by taking into account the fact that the subgroups of isometry Lie group of the metrics can be taken as one of the subgroups of the Drinfeld double (with Abelian duals) we look up the PL T-duality. To construct the dualizable metrics by the PL T-duality we find all subalgebras of Killing vectors that generate subgroup of isometries which acts freely and transitively on the manifolds defined by aforementioned $AdS$ families. We then obtain the dual backgrounds for these families of $AdS$ in such a way that we apply the usual rules of PL T-duality without further corrections. We have also investigated the conformal invariance conditions of the original backgrounds ($AdS$ families) and their dual counterparts. Finally, by using the T-duality rules proposed by Kaloper and Meissner (KM) we calculate the Abelian T-duals of BTZ black hole up to two-loop by dualizing on the coordinates $ φ$ and $ t $. When the dualizing is implemented by the shift of direction $φ$, we show that the horizons and singularity of the dual spacetime are the same as in charged black string derived by Horne and Horowitz without $α'$-corrections, whereas in dualizing on the coordinate $t$ we find a new three-dimensional black string whose structure and asymptotic nature are clearly determined. For this case, we show that the T-duality transformation changes the asymptotic behavior from $AdS_3$ to flat.

hep-th↗

arXiv2021

Yang-Baxter deformations of WZW model on the Heisenberg Lie group

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 $H_4$ WZW model are split into ten nonequivalent backgrounds including metric and $B$-field such that some of the metrics of these backgrounds can be transformed to the metric of $H_{4}$ WZW model while the antisymmetric $B$-fields are changed. The rest of the deformed metrics have a different isometric group structure than the $H_{4}$ WZW model metric. As an interesting result, it is shown that all new integrable backgrounds of the YB deformed $ H_4$ WZW model are conformally invariant up to two-loop order. In this way, we obtain the general form of the dilaton fields satisfying the vanishing beta-function equations of the corresponding $σ$-models.

hep-th↗

arXiv2021

T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in $α'$ 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 Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to $α'$-corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as $A_2$, $A_2 \oplus A_1$ and $SL(2, \mathbb{R})$. In this way, the PL self-duality of $AdS_3 \times \mathbb{R}$ space is discussed.

hep-th↗

arXiv2020

Cosmological string backgrounds from super Poisson-Lie T-plurality

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 $σ$-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, including $(2+1|2)$-dimensional metric, time-dependent dilaton and vanishing torsion, in a way that they satisfy the one-loop beta-function equations. Starting from the decompositions of semi-Abelian Drinfeld superdoubles (DSDs) generated by the $({\C}^3 +{\A})$ and $gl(1|1)$ Lie super bi-algebras we find the conformal duality/plurality chains of $2+1$-dimensional cosmological string backgrounds coupling with two fermionic fields. In particular, the new backgrounds obtained by the super PL T-plurality remain conformally invariant at one-loop level. This work can prompt many new insights into supergravity and obviously has interesting mathematical relations with double field theory.

hep-th↗