Classical Yang-Baxter equation from supergravity

Bakhmatov, Ilya; Kelekci, Özgür; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.

doi:10.1103/physrevd.98.021901

Cited by 40 publications

(82 citation statements)

References 71 publications

(121 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• It would be highly desirable to confirm our projector formula in a different framework, independent of Abelian T-duality. A natural setting could be the susy variations in β-supergravity recently discussed in [39].…”

Section: Discussionmentioning

confidence: 99%

SUSY and the bi-vector

et al. 2019

View full text Add to dashboard Cite

In this note we give an explicit formula for the preserved Killing spinors in deformed string theory backgrounds corresponding to integrable Yang-Baxter deformations realized via (sequences of) TsT transformations. The Killing spinors can be expressed only in terms of the bi-vector Θ which encodes the deformation. This formula is applicable to deformed backgrounds related to r-matrices of various ranks, including those that do not satisfy the unimodularity condition and give rise to backgrounds in generalized supergravity. We conjecture that our formula also remains valid for integrable deformations which are not realized via TsT transformations and motivate this conjecture by explicit examples.

show abstract

Section: Discussionmentioning

confidence: 99%

SUSY and the bi-vector

et al. 2019

View full text Add to dashboard Cite

show abstract

“…In fact, at two loops in the scheme of KM also b µν gets modified. 16 It is important to remark that already 14 The field redefinitions given in [45] relate the KM and the MT schemes only on-shell, but this is enough for our purposes, since we just want to make sure that we can generate solutions of the two-loop equations. 15 These are the redefinitions needed when we set the parameter q of [37] to zero.…”

Section: )mentioning

confidence: 99%

“…Therefore, in certain cases a sequence of TsT transformations can be implemented only in one precise order. Non-commuting sequences of TsT transformations are nice examples to study, because we can obtain explicit results by applying what is known about abelian T-duality and TsT, and at the same time be able to say something about NATD and more general YB deformations.In the remaining part of the introduction, we will summarize the main results obtained when expanding the two-loop equations to second order in the deformation parameter.2 These rules were first guessed, at the supergravity level and restricted to the case of vanishing NSNS flux, in [15] (see also [16]). 3 Note however that the form of the α ′ -corrections are only know in special cases and to low loop order, e.g.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Two-loop conformal invariance for Yang-Baxter deformed strings

Borsato

Wulff

2020

J. High Energ. Phys.

View full text Add to dashboard Cite

The so-called homogeneous Yang-Baxter (YB) deformations can be considered a non-abelian generalization of T-duality-shift-T-duality (TsT) transformations. TsT transformations are known to preserve conformal symmetry to all orders in α ′ . Here we argue that (unimodular) YB deformations of a bosonic string also preserve conformal symmetry, at least to two-loop order. We do this by showing that, starting from a background with no NSNS-flux, the deformed background solves the α ′ -corrected supergravity equations to second order in the deformation parameter. At the same time we determine the required α ′ -corrections of the deformed background, which take a relatively simple form. In examples that can be constructed using, possibly non-commuting sequences of, TsT transformations we show how to obtain the first α ′ -correction to all orders in the deformation parameter by making use of the α ′ -corrected T-duality rules. We demonstrate this on the specific example of YB deformations of a Bianchi type II background. sigma model with isometries. This was carried out for the Green-Schwarz superstring in [14] and rules for writing the supergravity background directly in terms of the R-matrix were derived. 2The simplest class of such YB deformations is when R is defined on an abelian subalgebra of the isometry algebra. In this case the deformation is equivalent to a T-duality-shift-T-duality (TsT) transformation [17]. These are also known as O(d, d)-transformations [18,19] and they have been argued to map a consistent string background to another consistent string background, i.e. there should exist corrections to the background fields such that the corrected background solves the α ′ -corrected supergravity equations to all orders in α ′ [20,21,22,23,24,25]. 3 Here we want to ask what happens for YB deformations in general at the quantum level. 4 Unimodular YB deformations are known to give a conformal theory at one loop, i.e. the background solves the (super)gravity equations. Here we will analyze the two-loop equations in the bosonic string case. For simplicity we will restrict to deformations of backgrounds with vanishing NSNS-flux. We will show, to second order in the deformation parameter, that the deformed background can be corrected so that it solves the 2-loop equations. Furthermore the correction to the background fields can be cast in a relatively simple form, giving hope that the result can be extended to all orders in the deformation parameter and perhaps higher orders in α ′ .Since the homogeneous YB deformations can be constructed using NATD, our results indicate that also NATD should preserve conformality at two loops, and possibly all orders in α ′ . Another piece of evidence for this comes from the recent analysis of renormalizability of deformed sigma models with two-dimensional target space in [28], and very recently [29]. Some of the deformations considered have a limit where they reduce to NATD and it was found that the models behave nicely beyond lowest order in α ′ suggesting that things should wor...

show abstract

“…is sufficient for the deformed fields G, B to be a solution of supergravity [22,23]. This allows to view the transformation (1.1) as a supergravity solution generating method, valid for generic spacetimes with isometries [24,25]. The reason that the classical Yang-Baxter equation (1.2) is instrumental in the d = 10 deformation prescription is ultimately that the two-dimensional string worldsheet theory exists behind the scenes of the supergravity approximation.…”

Section: Introductionmentioning

confidence: 99%

Tri-vector deformations in d = 11 supergravity

Bakhmatov

Deger

Musaev

et al. 2019

J. High Energ. Phys.

View full text Add to dashboard Cite

A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form M 4 × M 7 with the 4-form flux on M 4 is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS 4 ×S 7 solution in d = 11 supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS 4 × S 7 .

show abstract

Classical Yang-Baxter equation from supergravity

Cited by 40 publications

References 71 publications

SUSY and the bi-vector

SUSY and the bi-vector

Two-loop conformal invariance for Yang-Baxter deformed strings

Tri-vector deformations in d = 11 supergravity

Contact Info

Product

Resources

About