Yang-Baxter deformations and generalized supergravity -- A short summary

Abstract

Integrable deformations of type IIB superstring theory on ${\mathrm{AdS}}_5\times S^5$ have played an important role over the last years. The Yang-Baxter deformation is a systematic way of generating such integrable deformations. Since its introduction, this topic has seen important conceptual progress and has among others led to the intriguing discovery generalized supergravity, a new low-energy effective theory. This review endeavors to not only introduce the historical development of the Yang-Baxter deformation, but also its relation to generalized supergravity, non-geometric backgrounds, non-abelian T-duality and preserved Killing spinors. We supplement the general treatment with a wealth of explicit examples.

arXiv comment64 pages plus appendices. Invited review by J.Phys.A. Based on various papers of the authors

References in corpus (124)

• String Theory and Noncommutative Geometry
• 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
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• 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
• Background independent action for double field theory
• On integrability of the Yang-Baxter $\si$-model
• Large N Limit of Non-Commutative Gauge Theories
• Foundations of the AdS_5 x S^5 Superstring. Part I
• 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
• The gauge algebra of double field theory and Courant brackets
• Localization techniques in quantum field theories
• Non-Commutative Yang-Mills and the AdS/CFT Correspondence
• Heating up Galilean holography
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• 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
• 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
• On non-abelian T-dual geometries with Ramond fluxes
• On Nonabelian Duality
• Stringy differential geometry, beyond Riemann
• On Non-Abelian Duality
• 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
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Exotic branes and non-geometric backgrounds
• Abelian Yang-Baxter Deformations and TsT transformations
• 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
• Green-Schwarz Strings in TsT-transformed backgrounds
• Covariant action for a string in doubled yet gauged spacetime
• Integrable deformations of T-dual $\sigma$ models
• A Problem with Non-Abelian Duality
• Electric/Magnetic Deformations of S^3 and AdS_3, and Geometric Cosets
• T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map
• Integrability of classical strings dual for noncommutative gauge theories
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Supersymmetry and non-Abelian T-duality in type II supergravity
• β-supergravity: a ten-dimensional theory with non-geometric fluxes, and its geometric framework
• String theory of the Omega deformation
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Review of AdS/CFT Integrability, Chapter VI.1: Superconformal Symmetry
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• SO(d,d) Transformations of Ramond-Ramond Fields and Space-time Spinors
• Almost abelian twists and AdS/CFT
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• The Omega Deformation From String and M-Theory
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• Duality Versus Supersymmetry and Compactification
• 7-Branes and Higher Kaluza-Klein Branes
• Melvin solution in string theory
• Schrödinger geometries arising from Yang-Baxter deformations
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• Generalized gravity from modified DFT
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Non-Abelian Momentum-Winding Exchange
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Dualities, Twists, and Gauge Theories with Non-Constant Non-Commutativity
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• $T$-folds from Yang-Baxter deformations
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• Quantum deformations of the flat space superstring
• 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)
• Causal structures and holography
• Integrability in dipole-deformed N=4 super Yang-Mills
• String theory dualities from M theory
• On jordanian deformations of AdS_5 and supergravity
• Puzzles of eta-deformed AdS_5 x S^5
• Local $\beta$-deformations and Yang-Baxter sigma model
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality
• $I$ in generalized supergravity
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• Deformation independent open brane metrics and generalized theta parameters
• Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
• Warped anti-de Sitter spaces from brane intersections in type II string theory
• Canonical differential geometry of string backgrounds
• Weyl invariance of string theories in generalized supergravity backgrounds
• T-Duality of p-Branes
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Non-split and split deformations of AdS_5
• Tri-vector deformations in $d=11$ supergravity
• Unimodular jordanian deformations of integrable superstrings
• Deformed supersymmetric gauge theories from the fluxtrap background
• Timelike U-dualities in Generalised Geometry
• Integrable deformations of coupled sigma-models
• Holomorphic Chern-Simons theory and lambda models: PCM case
• Embedding the modified CYBE in Supergravity
• Generalized Supergravity Equations and Generalized Fradkin-Tseytlin Counterterm
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Deformation of $\mathcal{N}=4$ SYM with varying couplings via fluxes and intersecting branes
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Supersymmetric Gauge Theory with Space-time Dependent Couplings
• The Holographic Dual of the $\Omega$-background
• Killing spinors from classical r-matrices
• Classification of non-Riemannian doubled-yet-gauged spacetime
• U-duality in three and four dimensions
• Lax pairs for deformed Minkowski spacetimes
• SUSY and the bi-vector
• Extended Gauge Theory Deformations From~Flux~Backgrounds

Cited by in corpus (12)

• Integrable Deformations of Sigma Models
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Non-abelian U-duality at work
• Maximally Supersymmetric RG Flows in 4D and Integrability
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Integrability structures in string theory
• Polyvector deformations of Type IIB backgrounds
• Generalized Supergravity Equations for the WZW Model
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Constraining all possible Korteweg-de Vries type hierarchies
• Yang-Baxter structure of the extended space