Green-Schwarz mechanism and ${\alpha }^{\prime }$-deformed Courant brackets

Abstract

We establish that the unusual two-form gauge transformations needed in the Green-Schwarz anomaly cancellation mechanism fit naturally into an ${\alpha }^{\prime }$-deformed generalized geometry. The algebra of gauge transformations is a consistent deformation of the Courant bracket and features a nontrivial modification of the diffeomorphism group. This extension of generalized geometry emerged from a `doubled ${\alpha }^{\prime }$-geometry', which provides a construction of exactly gauge and T-duality invariant ${\alpha }^{\prime }$ corrections to the effective action.

arXiv comment22 pages, v2: refs. added

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• Heterotic $\alpha$'-corrections in Double Field Theory
• Heterotic Effective Action and Duality Symmetries Revisited
• The Odd story of ${\alpha }^{\prime }$-corrections
• Double Field Theory on Group Manifolds
• Factorization of Chiral String Amplitudes
• The Geometry, Branes and Applications of Exceptional Field Theory
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• Connections, Field Redefinitions and Heterotic Supergravity
• Quantum correction to generalized T-dualities
• Duality Invariance and Higher Derivatives
• T-duality Constraints on Higher Derivatives Revisited
• Amplitudes for left-handed strings
• Second order higher-derivative corrections in Double Field Theory
• T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in ${\alpha }^{\prime }$
• Generalized Dualities and Higher Derivatives
• O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• New non-perturbative de Sitter vacua in ${\alpha }^{\prime }$-complete cosmology
• Double Metric, Generalized Metric and ${\alpha }^{\prime }$-Geometry
• On the curious spectrum of duality invariant higher-derivative gravity
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Background Independent Double Field Theory at Order ${\alpha }^{\prime }$: Metric vs. Frame-like Geometry
• On Background Independence and Duality Invariance in String Theory
• T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm
• Cosmology at the top of the ${\alpha }^{\prime }$ tower
• The generalized Bergshoeff-de Roo identification II
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Green-Schwarz Mechanism for String Dualities
• T-duality equivalences beyond string theory
• ${\alpha }^{\prime }$-corrections and their double formulation
• Slowly rotating and the accelerating ${\alpha }^{\prime }$-corrected black holes in four and higher dimensions
• Extended Riemannian Geometry II: Local Heterotic Double Field Theory
• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
• Three-point Functions in Duality-Invariant Higher-Derivative Gravity
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• T-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Old Dualities and New Anomalies
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background
• Gauge Transformation of Double Field Theory for Open String
• Dimensional Reduction of the Generalized DBI
• An ${\alpha }^{\prime }$-complete theory of cosmology and its tensionless limit
• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• The Algebra of Diffeomorphisms from the World Sheet
• Non-geometric Five-branes in Heterotic Supergravity
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• Twisted C-brackets
• Loop Corrections in Double Field Theory: Non-trivial Dilaton Potentials
• Duality invariant string beta functions at two loops
• Massive strings from a haunted field theory
• Double Field Theory on Group Manifolds (Thesis)
• Moduli in General $SU(3)$-Structure Heterotic Compactifications
• Self-dual generalized metrics for pure $\mathcal{N}=1$ six-dimensional Supergravity
• Duality covariant field redefinitions