O(2,2) Transformations and the String Geroch Group

Abstract

The 1--loop string background equations with axion and dilaton fields are shown to be integrable in four dimensions in the presence of two commuting Killing symmetries and $\delta c=0$. Then, in analogy with reduced gravity, there is an infinite group that acts on the space of solutions and generates non--trivial string backgrounds from flat space. The usual $O(2,2)$ and $S$--duality transformations are just special cases of the string Geroch group, which is infinitesimally identified with the $O(2,2)$ current algebra. We also find an additional $Z_2$ symmetry interchanging the field content of the dimensionally reduced string equations. The method for constructing multi--soliton solutions on a given string background is briefly discussed.

Latex, 26p., CERN-TH.7144/94

References in corpus (30)

• Noncompact Symmetries in String Theory
• Duality, Quotients, and Currents
• Rotating Charged Black Hole Solution in Heterotic String Theory
• Elements of String Cosmology
• Twisting Classical Solutions in Heterotic String Theory
• $O(d,d)$-Covariant String Cosmology
• Manifestly $O(d,d)$ Invariant Approach to Space-Time Dependent String Vacua
• Rotating Dilaton Black Holes
• Generalized Duality in Curved String-Backgrounds
• Charged Black Holes in Two-Dimensional String Theory
• A Closed, Expanding Universe in String Theory
• Exact Duality Symmetries in CFT and String Theory
• Conformally Exact Metric and Dilaton in String Theory on Curved Spacetime
• An Equivalence Between Momentum and Charge in String Theory
• Marginal Deformations of WZNW and Coset Models from O(d,d) Transformation
• Strings on Curved Spacetimes: Black Holes, Torsion, and Duality
• Cosmological String Backgrounds from Gauged WZW Models
• String vacuum backgrounds with covariantly constant null Killing vector and 2d quantum gravity
• Generalized Duality and Singular Strings in Higher Dimensions
• Cosmological solutions with dilaton and maximally symmetric space in string theory
• Boosting Away Singularities from Conformal String Backgrounds
• A Superstring Theory in Four Curved Space-Time Dimensions
• Some Exact Solutions of String Theory in Four and Five Dimensions
• Finite sigma models and exact string solutions with Minkowski signature metric
• Global Analysis of New Gravitational Singularities in String and Particle Theories
• Four Dimensional Gravitational Backgrounds Based on N=4 c=4 Superconformal Systems
• On Cosmological String Backgrounds with Toroidal Isometries
• Duality, Marginal Perturbations and Gauging
• $SL(2,R)xSU(2)/R^2$ string model in curved spacetime and exact conformal results
• Duality and $O(d,d)$ Symmetries in String Theory

Cited by in corpus (50)

• Superstring Cosmology
• Symmetries of higher-order string gravity actions
• Rotating Kaluza-Klein Black Holes
• Duality Beyond the First Loop
• Supersymmetry and Dual String Solitons
• Dimensionally reduced gravity theories are asymptotically safe
• Integrable Systems in Stringy Gravity
• T-duality and world-sheet supersymmetry
• Matrix Dilaton-Axion for Heterotic String in Three Dimensions
• Completely integrable sector in 5D Einstein-Maxwell gravity and derivation of the dipole black ring solutions
• DUALITY SYMMETRY GROUP OF TWO DIMENSIONAL HETEROTIC STRING THEORY
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Anisotropic space-times in homogeneous string cosmology
• U-Duality and Symplectic Formulation of Dilaton-Axion Gravity
• HIDDEN SYMMETRIES OF TWO DIMENSIONAL STRING EFFECTIVE ACTION
• Classical Yang-Baxter Equation from Supergravity
• Integrability of Five Dimensional Minimal Supergravity and Charged Rotating Black Holes
• Solution generating in 5D Einstein-Maxwell-dilaton gravity and derivation of dipole black ring solutions
• Classical Symmetries of Some Two-Dimensional Models Coupled to Gravity
• Solitons of axion-dilaton gravity
• Ehlers Transformations and String Effective Action
• Symmetries of Heterotic String Theory
• Ehlers-Harrison transformations and black holes in Dilaton-Axion Gravity with multiple vector fields
• Spin-four N=7 W-Supergravity: S-fold and Double Copy Construction
• Inhomogeneous Einstein-Rosen String Cosmology
• Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
• Colliding String Waves and Duality
• Colliding Wave Solutions, Duality, and Diagonal Embedding of General Relativity in Two-Dimensional Heterotic String Theory
• Supersymmetry and Dualities
• Duality and Integrability of Two Dimensional String Effective Action
• Duality, Monodromy and Integrability of Two Dimensional String Effective Action
• Geroch Group Description of Black Holes
• Asymptotic Behaviour of Inhomogeneous String Cosmologies
• On Some New Black String Solutions in Three Dimensions
• Infinite-dimensional algebras in dimensionally reduced string theory
• Symmetries for generating string cosmologies
• Symplectic Gravity Models in Four, Three and Two Dimensions
• New integral equation form of integrable reductions of Einstein equations
• The Inverse Scattering Method, Lie-Backlund Transformations and Solitons for Low-energy Effective Field Equations of 5D String Theory
• Soliton solution in dilaton-Maxwell gravity
• Monodromy Matrix in the PP-Wave Limit
• Mirror Images of String Cosmologies
• Integrability of generalized (matrix) Ernst equations in string theory
• Geroch--Kinnersley--Chitre group for Dilaton--Axion Gravity
• Generation of the bosonic string theory solutions from the stationary Einstein fields via projection symmetry
• Charged Dual String Vacua from Interacting Rotating Black Holes Via Discrete and Nonlinear Symmetries
• Inhomogeneous M-Theory Cosmologies
• Master Ward Identity for Nonlocal Symmetries in D=2 Principal Chiral Models
• Solitons via Lie-Bäcklund Transformation for 5D Low-energy String Theory
• Kalb--Ramond dipole solution in low-energy bosonic string theory