$T$-folds from Yang-Baxter deformations

Abstract

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as $T$-fold by explicitly showing the associated $\mathrm{O}(D,D;\mathbb{Z})$ $T$-duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric $Q$-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian $T$-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a $T$-fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation.

arXiv comment47 pages

References in corpus (84)

• The Large N Limit of Superconformal Field Theories and Supergravity
• String Theory and Noncommutative Geometry
• Review of AdS/CFT Integrability: An Overview
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Target Space Duality in String Theory
• Double Field Theory
• Type IIB superstring action in AdS_5 x S^5 background
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• A Geometry for Non-Geometric String Backgrounds
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• On integrability of the Yang-Baxter $\si$-model
• Large N Limit of Non-Commutative Gauge Theories
• Nongeometric Flux Compactifications
• An integrable deformation of the AdS_5 x S^5 superstring action
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Lax Pair for Strings in Lunin-Maldacena Background
• New Supersymmetric String Compactifications
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Comments on string theory backgrounds with non-relativistic conformal symmetry
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Non-Commutative Yang-Mills and the AdS/CFT Correspondence
• Heating up Galilean holography
• Hot Spacetimes for Cold Atoms
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• 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
• On non-abelian T-dual geometries with Ramond fluxes
• Jordanian deformations of the AdS_5xS^5 superstring
• Plane Wave Limits and T-Duality
• On Nonabelian Duality
• On Non-Abelian Duality
• A ten-dimensional action for non-geometric fluxes
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Duality orbits of non-geometric fluxes
• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrability of the bi-Yang-Baxter sigma-model
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Abelian Yang-Baxter Deformations and TsT transformations
• Exotic branes and non-geometric backgrounds
• Integrable Deformations of Strings on Symmetric Spaces
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Large Gauge Transformations in Double Field Theory
• Yang-Baxter sigma models based on the CYBE
• Correlation functions in conformal Toda field theory II
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• Covariant action for a string in doubled yet gauged spacetime
• Manifest Duality in Low-Energy Superstrings
• A Problem with Non-Abelian Duality
• Integrable deformations of T-dual $\sigma$ models
• Integrability of classical strings dual for noncommutative gauge theories
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Poisson-Lie T-Duality in Double Field Theory
• A Jordanian deformation of AdS space in type IIB supergravity
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Almost abelian twists and AdS/CFT
• Remarks on Non-Abelian Duality
• (Non-)Abelian Gauged Supergravities in Nine Dimensions
• Melvin solution in string theory
• 7-Branes and Higher Kaluza-Klein Branes
• Schrödinger geometries arising from Yang-Baxter deformations
• Generalized gravity from modified DFT
• Dualities, Twists, and Gauge Theories with Non-Constant Non-Commutativity
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Generalized IIB supergravity from exceptional field theory
• On jordanian deformations of AdS_5 and supergravity
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections
• Integrable deformations of the AdS${}_5\times$S${}^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• $I$ in generalized supergravity
• The general gaugings of maximal d=9 supergravity
• Marginal and non-commutative deformations via non-abelian T-duality
• Timelike U-dualities in Generalised Geometry
• Generalized $\lambda$-deformations of AdS_p x S^p
• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• U-duality in three and four dimensions

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• Local $\beta$-deformations and Yang-Baxter sigma model
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• Tri-vector deformations in $d=11$ supergravity
• Dressing cosets and multi-parametric integrable deformations
• Classical Yang-Baxter equation from beta-supergravity
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Non-abelian tri-vector deformations in d=11 supergravity
• On non-Abelian T-duality for non-semisimple groups
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-abelian U-duality at work
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Embedding the modified CYBE in Supergravity
• Super Non-Abelian T-Duality
• $O(d,d)$ transformations preserve classical integrability
• Currents, charges and algebras in exceptional generalised geometry
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Analytical Structure of the Generalized $\lambda -$deformation
• Killing spinors from classical r-matrices
• Poisson-Lie transformations and Generalized Supergravity Equations
• SUSY and the bi-vector
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Generalised U-dual solutions via ISO(7) gauged supergravity
• Poisson-Lie identities and dualities of Bianchi cosmologies
• T-folds as Poisson-Lie plurals
• Non-isometric U-dualities
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$
• Generalised U-dual solutions in supergravity