arXiv subjects

Ali Eghbali

Publications and source records attributed to Ali Eghbali.

21 records · Page 2Linked to original sources

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↗

arXiv2018

Exact conformal field theories from mutually T-dualizable $σ$-models

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 $M \approx O \times \bf G$ and ${\tilde M} \approx O \times {\bf {\tilde G}}$, where $\bf G$ and ${\bf {\tilde G}}$ as two-dimensional real non-Abelian and Abelian Lie groups act freely on $M$ and $\tilde M$, respectively, while $O$ is the orbit of $\bf G$ in $M$. The findings of our study show that the original models are equivalent to Wess-Zumino-Witten (WZW) models based on the Heisenberg $(H_4)$ and $GL(2,\mathbb{R})$ Lie groups. In this way, some new T-dual backgrounds for these WZW models are obtained. For one of the duals of the $H_4$ WZW model, we show that the model is self-dual. In the case of the $GL(2,\mathbb{R})$ WZW model it is observed that the duality transformation changes the asymptotic behavior of solutions from $AdS_{3} \times \mathbb{R}$ to flat space. Then, the structure and asymptotic nature of the dual spacetime of this model including the horizon and singularity are determined. We furthermore get the non-critical Bianchi type III string cosmological model with a non-vanishing field strength from T-dualizable $σ$-models and show that this model describes an exact CFT (equivalent to the $GL(2,\mathbb{R})$ WZW model). After that, the conformal invariance of T-dual models up to two-loop order (first order in $α'$) is discussed.

hep-th↗

arXiv2015

Solution of the equations of motion for a super non-Abelian sigma model in curved background by the super Poisson-Lie T-duality

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 by the super Poisson-Lie T-duality. To find the solution of the flat model we use the transformation of supercoordinates, transforming the metric into a constant one, which is shown to be a supercanonical transformation. Then, using the super Poisson-Lie T-duality transformations and the dual decomposition of elements of Drinfel'd superdouble, the solution of the equations of motion for the dual sigma model is obtained. The general form of the dilaton fields satisfying the vanishing $β-$function equations of the sigma models is found. In this respect, conformal invariance of the sigma models built on the Drinfel'd superdouble $((C^1_1+A),I_{(2|2)})$ is guaranteed up to one-loop, at least.

hep-th↗