Quantum correction to generalized T-dualities

Abstract

Poisson-Lie duality is a generalization of abelian and non-abelian T-duality, and it can be viewed as a map between solutions of the low-energy effective equations of string theory, i.e. at the (super)gravity level. We show that this fact extends to the next order in ${\alpha }^{\prime }$ (two loops in $\sigma$-model perturbation theory) provided that the map is corrected. The ${\alpha }^{\prime }$-correction to the map is induced by the anomalous Lorentz transformations of the fields that are necessary to go from a doubled $O(D,D)$-covariant formulation to the usual (super)gravity description.

arXiv comment4 pages, plus 4 pages of supplemental material. 1 figure. Version 2: typos corrected, comments and references added. Title changed following a request by the journal's editor. Published version

References in corpus (36)

• Target Space Duality in String Theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Dual Non-Abelian Duality and the Drinfeld Double
• Double Field Theory: A Pedagogical Review
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• On Nonabelian Duality
• On Non-Abelian Duality
• Doubled α'-Geometry
• On the Riemann Tensor in Double Field Theory
• T-duality and ${\alpha }^{\prime }$-corrections
• Double Field Theory at Order ${\alpha }^{\prime }$
• Duality Beyond the First Loop
• Integrable deformations of T-dual $\sigma$ models
• Frame-like Geometry of Double Field Theory
• Poisson-Lie T-Duality in Double Field Theory
• Doubled aspects of generalised dualities and integrable deformations
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Poisson-Lie T-plurality
• The Odd story of ${\alpha }^{\prime }$-corrections
• Remarks on Non-Abelian Duality
• Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Poisson-Lie T-Duality: the Path-Integral Derivation
• Quantum Poisson-Lie T-duality and WZNW model
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Poisson-Lie Duality in the String Effective Action
• Green-Schwarz Mechanism for String Dualities
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Two-loop conformal invariance for Yang-Baxter deformed strings

Cited by in corpus (28)

• Integrable Deformations of Sigma Models
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• The generalized Bergshoeff-de Roo identification II
• RG flow of integrable $\mathcal{E}$-models
• ${\alpha }^{\prime }$-corrections and their double formulation
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Consistent Truncations and Dualities
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• The ${\alpha }^{\prime 2}$ correction from double field theory
• Jacobi-Lie T-plurality
• Dual description of $\eta$-deformed OSP sigma models
• The twisted story of worldsheet scattering in $\eta$-deformed $Ad{S}_5\times S^5$
• Poisson-Lie transformations and Generalized Supergravity Equations
• T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach
• T-duality and T-folds for point particles
• Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations
• On 10 dimensional Exceptional Drinfel'd Algebras
• Integrability structures in string theory
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• An Algebraic Classification of Solution Generating Techniques
• Plane-parallel waves as Jacobi-Lie models
• Supergravity solution-generating techniques and canonical transformations of $\sigma$-models from $O(D,D)$
• Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Half-maximal Extended Drinfel'd Algebras
• Duality covariant field redefinitions