The ${\alpha }^{\prime 2}$ correction from double field theory

Abstract

It is known that the order ${\alpha }^{\prime }$ correction to the tree-level effective action for the bosonic and heterotic string can be described in the framework of Double Field Theory (DFT). Here we determine the DFT action and transformations at order ${\alpha }^{\prime 2}$ by a direct calculation. The result is vastly simpler than previous proposals. We show that this correction reproduces the known ${\alpha }^{\prime 2}$ correction to the heterotic string effective action. The relation of our action to an (implicit) all order proposal coming from the so-called generalized Bergshoeff-de Roo identification is also discussed.

arXiv comment39 pages; v2: Added sec 4.2 detailing the relation to the original generalized Bergshoeff-de Roo identification. Published version

References in corpus (31)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Double Field Theory and N=4 Gauged Supergravity
• Exploring Double Field Theory
• Manifestly $O(d,d)$ Invariant Approach to Space-Time Dependent String Vacua
• Doubled α'-Geometry
• Gauged Double Field Theory
• Double Field Theory Formulation of Heterotic Strings
• On the Riemann Tensor in Double Field Theory
• T-duality and ${\alpha }^{\prime }$-corrections
• Double Field Theory at Order ${\alpha }^{\prime }$
• Duality Beyond the First Loop
• Generalised geometry for string corrections
• Solution--Generating Transformations and the String Effective Action
• Frame-like Geometry of Double Field Theory
• Heterotic $\alpha$'-corrections in Double Field Theory
• The Odd story of ${\alpha }^{\prime }$-corrections
• Quantum correction to generalized T-dualities
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• ${\alpha }^{\prime }$-corrected Poisson-Lie T-duality
• Quadratic ${\alpha }^{\prime }$-Corrections to Heterotic Double Field Theory
• Generalized Dualities and Higher Derivatives
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• The generalized Bergshoeff-de Roo identification II
• Supersymmetry, T-duality and Heterotic ${\alpha }^{\prime }$-corrections
• Extended Riemannian Geometry II: Local Heterotic Double Field Theory
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• Relaxing unimodularity for Yang-Baxter deformed strings
• String theory at order ${\alpha }^{\prime 2}$ and the generalized Bergshoeff-de Roo identification
• Duality covariant field redefinitions

Cited by in corpus (5)

• Higher Derivative Supergravities in Diverse Dimensions
• Double Field Theory with matter and the generalized Bergshoeff-de Roo identification
• T-duality building blocks for ${\alpha }^{\prime }$ string corrections
• Higher-derivative Heterotic Kerr-Sen Black Holes
• Plane-parallel waves as Jacobi-Lie models