We show that the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order α ′ 3 , with overall coefficient proportional to ζ(3), is not invariant under standard O(9, 9) transformations. This is in conflict with 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 α ′ . Possible resolutions of this puzzle are discussed.
Generalized dualities had an intriguing incursion into Double Field Theory (DFT) in terms of local O(d, d) transformations. We review this idea and use the higher derivative formulation of DFT to compute the first order corrections to generalized dualities. Our main result is a unified expression that can be easily specified to any generalized T-duality (Abelian, non-Abelian, Poisson-Lie, etc.) or deformations such as Yang-Baxter, in any of the theories captured by the bi-parametric deformation (bosonic, heterotic strings and HSZ theory), in any supergravity scheme related by field redefinitions. The prescription allows further extensions to higher orders. As a check we recover some previously known particular examples.
We show how the gauge and field structure of the tensor hierarchies in Double and E 7(7)Exceptional Field Theory fits into L ∞ algebras. Special attention is paid to redefinitions, the role of covariantly constrained fields and intertwiners. The results are connected to Gauged Supergravities through generalized Scherk-Schwarz reductions. We find that certain gaugingdependent parameters generate trivial gauge transformations, giving rise to novel symmetries for symmetries that are absent in their ungauged counterparts.
The O(d, d) invariant worldsheet theory for bosonic string theory with d abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of motion of the Maharana-Schwarz action. We give a self-contained introduction into the required techniques, including beta functions, the Weyl anomaly for two-dimensional sigma models and the background field method. This sets the stage for a sequel to this paper on generalizations to higher loops and α′ corrections.
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