WZW models as mutual super Poisson-Lie T-dual sigma models

Eghbali, A.; Rezaei-Aghdam, A.

doi:10.48550/arxiv.1303.4069

Cited by 10 publications

(20 citation statements)

References 23 publications

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“…Up to now, several attempts in the construction of Poisson-Lie T-dual sigma models [7,8] and investigation of Poisson-Lie symmetry of some WZW models [9,10] have been performed. The generalization of Poisson-Lie T-dual sigma models on supermanifolds has been done in [11,12,13]. Also, canonical equivalence of the Poisson-Lie T-dual sigma models already has been shown in [1,2,14,15], but in general the quantization of these T-dual sigma models is still a challenging problem (the quantum equivalence of the Poisson-Lie T-dual sigma models under one-loop renormalization group flow is studied for some special examples in [7,9,16] and has been shown in general in [17] and [18]).…”

Section: Introductionmentioning

confidence: 99%

Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds

Rezaei-Aghdam

Sephid

2018

Nuclear Physics B

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Using the concept of Jacobi-Lie group and Jacobi-Lie bialgebra, we generalize the definition of Poisson-Lie symmetry to Jacobi-Lie symmetry. In this regard, we generalize the concept of Poisson-Lie T-duality to Jacobi-Lie T-duality and present Jacobi-Lie T-dual sigma models on Lie groups, which have Jacobi-Lie symmetry. Using this symmetry, new cases of duality appear and some examples are given. This generalization may provide insights to understand the quantum features of Poisson-Lie T-duality, in a more satisfactory way.

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Section: Introductionmentioning

confidence: 99%

Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds

Rezaei-Aghdam

Sephid

2018

Nuclear Physics B

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“…Before proceeding to construct the metric, let us introduce the (C 3 +A ) Lie superalgebra [15]. The (C 3 +A ) is a four-dimensional Lie superalgebra of the type (2|2) which has supersymmetric, ad-invariant and non-degenerate metric on its structure [32]. It is spanned by the set of generators {T 1 , T 2 ; T 3 , T 4 } with gradings; grade(T 1 )=grade(T 2 ) = 0 and grade(T 3 )=grade(T 4 ) = 1, which fulfill the following non-zero (anti)commutation rules [15]:…”

Section: Cosmological String Backgrounds From the (C 3 + A) Lie Super...mentioning

confidence: 99%

Cosmological string backgrounds from super Poisson-Lie T-plurality

Eghbali

2020

Preprint

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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 leftinvariant 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.

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“…Klimčik and Ševera proposed a generalization of T-duality, or the socalled PL T-duality [20,21], which allows the duality to be performed on a target space without isometries. Afterwards, PL T-duality transformations could be generalized to the Lie supergroups [22] as well as supermanifolds [23], in such a way that super PL symmetry of the WZW models based on some of the Lie supergroups of superdimension (2|2) was studied [24,25]. Of course, in the Lie groups case, PL symmetry of the WZW models was already been studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Eghbali,

Naderi,

Rezaei-Aghdam

2020

Preprint

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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 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. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by twoand three-dimensional non-Abelian Lie groups such as A 2 , A 2 ⊕ A 1 and SL(2, R). It is shown that the non-Abelian dual models are conformally invariant to the order α only for the case of β = 1. Following that, the PL self-duality of AdS 3 × R space (β = 1 case) is discussed.

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WZW models as mutual super Poisson-Lie T-dual sigma models

Cited by 10 publications

References 23 publications

Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds

Jacobi–Lie symmetry and Jacobi–Lie T-dual sigma models on group manifolds

Cosmological string backgrounds from super Poisson-Lie T-plurality

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

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