Yang-Baxter Deformation as an O(d,d) Transformation

Abstract

The rules for Yang-Baxter (YB) deformation for a generic Green-Schwarz string sigma model has been obtained recently. We show that the deformation can be described through the action of a coordinate dependent $O(d,d)$ matrix on the target space fields both in the NS-NS and the RR sectors, generalizing previous results. This enables us to show that the YB deformed fields can be regarded as duality twisted fields in the context of Gauged Double Field Theory (GDFT). We compute the fluxes associated with the twist and show that the conditions on the R-matrix determining the YB deformation give rise to conditions for the fluxes on the GDFT side. More precisely, we show that YB deformation is a process which takes a solution of DFT with geometric flux associated with the isometry group $G$ and deforms it to another solution of DFT with vanishing R-flux and non-vanishing Q-flux given by the structure constants of the dual Lie algebra determined by the R-matrix. We also show that the non-unimodularity of the R-matrix forces the generalized dilaton field to pick up a linear dependence on the winding type coordinates of DFT, implying that the corresponding target space fields satisfy the field equations of DFT in the generalized supergravity frame. This provides a new perspective on the relation between the non-unimodularity of the R-matrix, the trace of the Q-flux and the generalized supergravity equations.

arXiv commentreferences added; revised Introduction; minor corrections; some of the discussions clarified, section 4.3 on generalised supergravity equations expanded, one reference added

References in corpus (61)

• String Theory and Noncommutative Geometry
• Target Space Duality in String Theory
• Double Field Theory
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Generalized metric formulation of double field theory
• A Geometry for Non-Geometric String Backgrounds
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Lax Pair for Strings in Lunin-Maldacena Background
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Double Field Theory and N=4 Gauged Supergravity
• Exploring Double Field Theory
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Jordanian deformations of the AdS_5xS^5 superstring
• T-Duality, Space-time Spinors and R-R Fields in Curved Backgrounds
• Double Field Theory of Type II Strings
• Gauged Double Field Theory
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Abelian Yang-Baxter Deformations and TsT transformations
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• The effective action of Double Field Theory
• Integrable deformations of T-dual $\sigma$ models
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• Doubled aspects of generalised dualities and integrable deformations
• Almost abelian twists and AdS/CFT
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• Double Field Theory, T-Duality, and Courant Brackets
• Comments on T-dualities of Ramond-Ramond Potentials
• Generalized gravity from modified DFT
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Lunin-Maldacena Deformations With Three Parameters
• $T$-folds from Yang-Baxter deformations
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Generalized IIB supergravity from exceptional field theory
• Weyl invariance for generalized supergravity backgrounds from the doubled formalism
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Classical Yang-Baxter Equation from Supergravity
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Local $\beta$-deformations and Yang-Baxter sigma model
• Integrable deformations of the AdS${}_5\times$S${}^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• $I$ in generalized supergravity
• Tri-vector deformations in $d=11$ supergravity
• Marginal and non-commutative deformations via non-abelian T-duality
• Classical Yang-Baxter equation from beta-supergravity
• On non-Abelian T-duality for non-semisimple groups
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Embedding the modified CYBE in Supergravity
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• Beta, Dipole and Noncommutative Deformations of M-theory Backgrounds with One or More Parameters
• Massive Deformations of Type IIA Theory Within Double Field Theory

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