Type II superstring in doubled superspace

Bandos, Igor A.

doi:10.1002/prop.201500055

Cited by 5 publications

(7 citation statements)

References 15 publications

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“…A manifestly T -duality covariant formulations of string theory, the so-called double sigma model (DSM), has been developed in [60,[82][83][84][85][86][87] for the bosonic string. More recently, the DSM for the GS type II superstring theory was formulated in [64] (see also [60][61][62][63]65] for other approaches to supersymmetric DSMs). The action by Park, in our convention, is given by…”

Section: T -Duality-invariant Green-schwarz Actionmentioning

confidence: 99%

Local β-deformations and Yang-Baxter sigma model

Sakamoto

Sakatani

2018

J. High Energ. Phys.

104

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Homogeneous Yang-Baxter (YB) deformation of AdS 5 × S 5 superstring is revisited.We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to β-deformations of the AdS 5 × S 5 background when the classical r-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10, 10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing H-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study β-deformations of H-fluxed AdS backgrounds and obtain various solutions of (generalized) type II Yang-Baxter (YB) sigma model was originally introduced by Klimčík [1] as a class of Poisson-Lie symmetric sigma models. It is characterized by a classical r-matrix that satisfies the modified classical YB equation (mCYBE). It was later shown to be integrable by constructing the Lax pair [2]. The original YB sigma model can be applied only to sigma models on group manifolds, but it was later generalized to coset sigma models in [3] and to the case of the homogeneous classical YB equation (CYBE) in [4].An interesting application of YB deformations is an integrable deformation of type IIB superstring theory on the AdS 5 × S 5 background [5][6][7], that has been studied in the context of the AdS/CFT correspondence. Through various examples [8][9][10][11][12][13], it turned out that, when we employ an Abelian classical r-matrix, the YB-deformed AdS 5 ×S 5 superstring can be described as type IIB superstring on a TsT-transformed 1 AdS 5 × S 5 background [14-20] (see [21] for a clear explanation and generalizations). Namely, Abelian YB deformation was found to be equivalent to a TsT-transformation. For non-Abelian classical r-matrices, the deformations of the AdS 5 × S 5 background have not been understood clearly; some deformed backgrounds were obtained through non-commuting TsT-transformations (see for example [22]) and some were obtained through a combination of diffeomorphisms and T -dualities [23], but it is not clear whether an arbitrary YB deformation can be realized as a combination of Abelian Tdualities and gauge symmetries of the supergravity (it was recently shown in [24][25][26][27][28] that YB deformations can be also reproduced from non-Abelian T -dualities [29][30][31][32][33][34][35][36][37][38]). As shown in a seminal paper [22], at least when an r-matrix satisfies a certain criterion called unimodularity, the deformed AdS 5 × S 5 background are solutions of type IIB supergravity. Moreover, for a non-unimodular r-matrix, the deformed AdS 5 × S 5 background was shown to satisfy the generalized supergravity equations of motion (GSE) [39,40], and a Killing vector I m appearing in the GSE was determined for a general r-matrix. In a recent ...

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Section: T -Duality-invariant Green-schwarz Actionmentioning

confidence: 99%

Local β-deformations and Yang-Baxter sigma model

Sakamoto

Sakatani

2018

J. High Energ. Phys.

104

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“…The modification of the definition of C by the extraK m terms that we propose is rooted in the analysis of the DFT constraints and equations of motion. We do not attempt a first principles derivation of a non-abelian Buscher procedure in the DFT setting and solvinig the supergravity constraints in the superfield formalism for DFT [37][38][39][40], leaving that for a separate work. In the following section we do check that the fermionic non-abelian T-duals defined by (2.2), (2.5) are actually solutions of DFT.…”

Section: Jhep09(2021)135mentioning

confidence: 99%

“…For doubled superspace constructions see[37][38][39][40] 4. They may depend on spectator fields in case when bosonic dimension of the supergroup is less than ten.…”

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confidence: 99%

Non-abelian fermionic T-duality in supergravity

Astrakhantsev

Bakhmatov

Musaev

2021

J. High Energ. Phys.

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Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric. Comparison with alternative treatment based on sigma models on supercosets shows consistency.

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“…The second term may be 3 For doubled superspace constructions see [50][51][52]. 4 They may depend on spectator fields in case when bosonic dimension of the supergroup is less than ten.…”

Section: Sigma Model Perspectivementioning

confidence: 99%

Non-abelian fermionic T-duality in supergravity

Astrakhantsev,

Bakhmatov,

Musaev

2021

Preprint

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Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric.Comparison with alternative treatment based on sigma models on supercosets shows consistency.

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Type II superstring in doubled superspace

Cited by 5 publications

References 15 publications

Local β-deformations and Yang-Baxter sigma model

Local β-deformations and Yang-Baxter sigma model

Non-abelian fermionic T-duality in supergravity

Non-abelian fermionic T-duality in supergravity

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