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

References in corpus (13)

• Double Field Theory
• R^4, purified
• The One-Loop Five-Graviton Amplitude and the Effective Action
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• alpha'-Corrections to Heterotic Superstring Effective Action Revisited
• Four-derivative couplings via T-duality constraint
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• General String Cosmologies at Order ${\alpha }^{\prime }{}^3$
• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• T-duality equivalences beyond string theory
• Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace
• $O(9,9)$ symmetry of NS-NS couplings at order ${\alpha }^{\prime 3}$
• $O(25,25)$ symmetry of bosonic string theory at order ${\alpha }^{\prime 2}$

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