Marginal deformations of WZW models and the classical Yang-Baxter equation

Abstract

We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE), give rise to marginal current-current deformations when applied to the Wess-Zumino-Witten (WZW) model. For non-compact groups these marginal deformations are more general than the ones usually considered, since they can involve a non-abelian current subalgebra. We classify such deformations of the AdS(3) x S(3) string.

arXiv comment29 pages; v2: Clarification of marginality condition from conformal pert. theory and of non-SUGRA solution (R4). Appendix E improved. Published version

References in corpus (58)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• 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
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• More Comments on String Theory on AdS_3
• The Worldsheet Dual of the Symmetric Product CFT
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• 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
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• On Non-Abelian Duality
• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• Abelian Yang-Baxter Deformations and TsT transformations
• Exact Duality Symmetries in CFT and String Theory
• Green-Schwarz Strings in TsT-transformed backgrounds
• Superstrings on NS5 backgrounds, deformed AdS3 and holography
• Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation
• Integrable deformations of T-dual $\sigma$ models
• Electric/Magnetic Deformations of S^3 and AdS_3, and Geometric Cosets
• Integrability of classical strings dual for noncommutative gauge theories
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Integrable double deformation of the principal chiral model
• Doubled aspects of generalised dualities and integrable deformations
• $J\bar{T}$ deformed $CF{T}_2$ and String Theory
• Strings on warped AdS${}_3$ via $T\bar{J}$ deformations
• Almost abelian twists and AdS/CFT
• Three-dimensional black holes from deformed anti-de Sitter
• Remarks on Non-Abelian Duality
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Current-Current Deformations of Conformal Field Theories, and WZW Models
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• A truly marginal deformation of SL(2,R) in a null direction
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• The Spectrum of Strings on Warped AdS_3 x S^3
• On a `universal' class of WZW-type conformal models
• Classical Yang-Baxter Equation from Supergravity
• Local $\beta$-deformations and Yang-Baxter sigma model
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly
• Duality, Marginal Perturbations and Gauging
• Heterotic strings on homogeneous spaces
• String Theory, Black Holes, and SL(2,R) Current Algebra
• Hamiltonian Approach to Poisson Lie T-Duality
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Symmetries of perturbed conformal field theories
• String Theory: exact solutions, marginal deformations and hyperbolic spaces

Cited by in corpus (20)

• Integrable Deformations of Sigma Models
• $T\bar{T}$ deformations as TsT transformations
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Glue-on AdS holography for $T\bar{T}$-deformed CFTs
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• $T\bar{T}$-deformation and Liouville gravity
• Extremal surfaces in glue-on AdS/$T\bar{T}$ holography
• Yang-Baxter deformations and generalized supergravity -- A short summary
• $O(d,d)$ transformations preserve classical integrability
• On the universal behavior of $T\bar{T}$-deformed CFTs: single and double-trace partition functions at large $c$
• Relaxing unimodularity for Yang-Baxter deformed strings
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Charting the Conformal Manifold of Holographic CFT${}_2$'s
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• The on-shell action of supergravity & the B-side of TsT and single-trace $T\bar{T}$