T-duality and hints of generalized geometry in string ${\alpha }^{\prime }$ corrections

Abstract

We examine the structure of higher-derivative string corrections under a cosmological reduction and make connection to generalized geometry and T-duality. We observe that, while the curvature $R_{\nu \rho \sigma }^{\mu }({\Omega }_{+})$ of the generalized connection with torsion, ${\Omega }_{+}=\Omega +\frac{1}{2}H$, is an important component in forming T-duality invariants, it is necessarily incomplete by itself. We revisit the tree-level ${\alpha }^{\prime }{R}^2$ corrections to the bosonic and heterotic string in the language of generalized geometry and explicitly demonstrate that additional $H$-field couplings are needed to restore T-duality invariance. We also comment on the structure of the T-duality completion of tree-level ${\alpha }^{\prime 3}{R}^4$ in the type II string.

32 pages

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Cited by in corpus (5)

• Higher Derivative Supergravities in Diverse Dimensions
• T-duality building blocks for ${\alpha }^{\prime }$ string corrections
• Higher-derivative couplings and torsional Riemann curvature
• Higher-derivative Heterotic Kerr-Sen Black Holes
• Consistent Four-derivative Heterotic Truncations and the Kerr-Sen Solution