Double Field Theory at Order $α'$

We investigate $α'$ corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled $α'$-geometry" gives $α'$-deformed gauge transformations arising in the Green-Schwarz anomaly cancellation mechanism but does not apply to bosonic strings. These require a different deformation of the duality-covariantized Courant bracket which governs the gauge structure. This is revealed by examining the $α'$ corrections in the gauge algebra of closed string field theory. We construct a four-derivative cubic double field theory action invariant under the deformed gauge transformations, giving a first glimpse of the gauge principle underlying bosonic string $α'$ corrections. The usual metric and $b$-field are related to the duality covariant fields by non-covariant field redefinitions.

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