The Odd story of α′-corrections

Abstract

The α ′ -deformed frame-like Double Field Theory (DFT) is a T-duality and gauge invariant extension of DFT in which generalized Green-Schwarz transformations provide a gauge principle that fixes the higher-derivative corrections. It includes all the first order α ′ -corrections of the bosonic and heterotic string low energy effective actions and of the Hohm-Siegel-Zwiebach α ′geometry. Here we gauge this theory and parameterize it in terms of a frame, a two-form, a dilaton, gauge vectors and scalar fields. This leads to a unified framework that extends the previous construction by including all duality constrained interactions in generic (gauged/super)gravity effective field theories in arbitrary number of dimensions, to first order in α ′ .

Duality invariant cosmology to all orders in α′

“…Such corrections have been computed to the first few orders in the 1980's [8][9][10], but a complete computation or classification of these corrections is presently out of reach. In recent years duality-covariant formulations of the string spacetime theories (double field theory [11][12][13][14]) have been used to make progress in describing α 1 corrections, see [15][16][17][18][19][20][21]. These developments hint at a completely novel kind of geometry where the diffeomorphism invariance of general relativity is replaced by a suitably generalized notion of diffeomorphisms, which in turn partly determines the α 1 corrections.…”

O(d, d) covariant string cosmology to all orders in α′

“…On the other hand, the first order α -corrections to supergravity were computed in the late 1980's [13,14,15], and in past years the use of dualities have helped the calculation of corrections in Double Field Theory (DFT) (see [16,17] for original articles on DFT and [18,19] for reviews). For α -corrections from DFT see [20,21,22,23], and references therein.…”

Green-Schwarz Mechanism for String Dualities

“…The reduction of α ′ -deformed double field theory has been investigated in Ref. [17], however, without extracting the consequences for the realization of O(d, d, R) in the dimensional reduction of conventional (non-extended) theories.…”

“…17) whereĨ 0 ,Ĩ 1 denote the actions (2.5) and(2.12), respectively, in which we have replaced all 3-form curvatures H µνρ by the deformationH µνρ ≡ H µνρ − α ′ Ω µνρ . (2.18) Indeed, this deformation of the lowest order action (2.5) precisely produces the non-invariant term (2.13) at order α ′ while the deformation of Eq.…”