String Dualities at Order ${\alpha }^{\prime 3}$

Abstract

We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order ${\alpha }^{\prime 3}$, with overall coefficient proportional to $\zeta (3)$, and show that it is compatible with an $O(9,9)$ symmetry. This confirms the general result in string theory, due to Sen, that classical string theory with $d$-dimensional translation invariance admits an $O(d,d)$ symmetry to all orders in ${\alpha }^{\prime }$.

10 pages, v2: Major changes. Puzzle alluded to in the original title has been resolved by finding a computational mistake. Corrected result: the ${\alpha }^{\prime 3}$ corrections with coefficient $\zeta (3)$ are compatible with continuous $O(9,9)$ symmetry. Details of computation and references added, v3: version published in PRL

References in corpus (25)

• Elements of String Cosmology
• Duality and Dilaton
• Manifestly $O(d,d)$ Invariant Approach to Space-Time Dependent String Vacua
• Symmetries of higher-order string gravity actions
• Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
• Double Field Theory at Order ${\alpha }^{\prime }$
• Duality Beyond the First Loop
• Duality Invariant Cosmology to all Orders in ${\alpha }^{\prime }$
• Solution--Generating Transformations and the String Effective Action
• The Supersymmetric Effective Action of the Heterotic String in Ten Dimensions
• Heterotic Effective Action and Duality Symmetries Revisited
• The Odd story of ${\alpha }^{\prime }$-corrections
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• T-duality Constraints on Higher Derivatives Revisited
• Non-singular string cosmology via ${\alpha }^{\prime }$ corrections
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• String Cosmology backgrounds from Classical String Geometry
• New non-perturbative de Sitter vacua in ${\alpha }^{\prime }$-complete cosmology
• $R^4$ terms in supergravities via T-duality constraint
• de Sitter, ${\alpha }^{\prime }$-Corrections & Duality Invariant Cosmology
• Green-Schwarz Mechanism for String Dualities
• Higher Order Conformal Invariance of String Backgrounds Obtained by O(d,d) Transformations
• Solution of the Size and Horizon Problems from Classical String Geometry
• O(d,d) invariance at two and three loops
• S-duality invariant dilaton couplings at order ${\alpha }^{\prime 3}$

Cited by in corpus (23)

• A master exceptional field theory
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• Cosmological ${\alpha }^{\prime }$-corrections from the functional renormalization group
• Duality-invariant extensions of Einstein-Maxwell theory
• Cosmology at the top of the ${\alpha }^{\prime }$ tower
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• Non-singular pre-big bang scenarios from all-order ${\alpha }^{\prime }$ corrections
• From the string vacuum to FLRW or de Sitter via ${\alpha }^{\prime }$ corrections
• $O(9,9)$ symmetry of NS-NS couplings at order ${\alpha }^{\prime 3}$
• Completing $R^4$ using $O(d,d)$
• T-duality and hints of generalized geometry in string ${\alpha }^{\prime }$ corrections
• Beta functions for the duality-invariant sigma model
• $O(25,25)$ symmetry of bosonic string theory at order ${\alpha }^{\prime 2}$
• T-duality building blocks for ${\alpha }^{\prime }$ string corrections
• An ${\alpha }^{\prime }$-complete theory of cosmology and its tensionless limit
• 2D Black Holes, Bianchi I Cosmologies, and ${\alpha }^{\prime }$
• Non-linear stability of ${\alpha }^{\prime }$-corrected Friedmann equations
• Duality invariant string beta functions at two loops
• Higher-derivative Heterotic Kerr-Sen Black Holes
• Consistent Four-derivative Heterotic Truncations and the Kerr-Sen Solution
• Black hole thermodynamics at 4 derivatives, natural variables and BPS limits
• Universal Box Operator: $\mathbf{O}(D,D)$-Symmetry and ${\alpha }^{\prime }$-Corrections
• Revisiting Schwarzschild black hole singularity through string theory