String Dualities at Order α′3

Abstract

We show that the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order α ′ 3 , with overall coefficient proportional to ζ(3), is not invariant under standard O(9, 9) transformations. This is in conflict with the general result in string theory, due to Sen, that classical string theory with d-dimensional translation invariance admits an O(d, d) symmetry to all orders in α ′ . Possible resolutions of this puzzle are discussed.

Cosmology at the top of the α′ tower

“…Note that 'non-singular' refers to the behaviour in the Einstein frame, so the solution can still have a singular behaviour in the string frame -the quest for non-singular solutions is only well defined once the frame in which this property holds is properly specified. 18 We will now turn to the question of trying to find actual solutions that could effectively violate the NEC and be non-singular.…”

“…This is known as the discrete scale factor duality [11], which is generalized to the continuous group 1 O(d, d) in d spatial dimensions [12,13]. The duality is proved to hold to all order in α [14] (see [15][16][17][18] for explicit verifications at finite orders in α ), hence suggesting O(d, d) symmetry may be imposed at the action level to help one construct a cosmological theory 2 that could include α corrections to all orders. This is what was achieved by Hohm & 1 Here and throughout, we assume the group with real elements, i.e.…”

Duality-invariant extensions of Einstein-Maxwell theory

“…For instance, string theory compactified on a torus is invariant under T-duality, which implies the invariance of the lower-dimensional stringy effective actions under the group O(d, d). This symmetry is claimed to be preserved at all orders in the higher-derivative α -expansion [1], and explicit confirmation of this has been reported for the lowest-order terms [2][3][4][5][6][7]. However, the computation of these α corrections from first principles is a complicated problem, and, instead, it turns out that one can use duality invariance to constrain the higher derivative corrections that appear in the stringy effective actions -see, e.g., [8][9][10].…”

Supersymmetry, T-duality and heterotic α′-corrections

“…In particular, the effective field theories for the massless string fields exhibit a global O(n, n; R) symmetry when the fields are independent of n spatial coordinates. This continuous T-duality symmetry holds to all orders in α [38] (see also [39][40][41][42][43][44][45][46][47]) and it has been explicitly displayed recently for the quadratic and some of the quartic interactions of the bosonic fields in [48,49]. This feature motivated the construction of field theories with T-duality covariant structures, such as double field theory (DFT) [50][51][52][53][54][55][56] and generalized geometry [57,58], which provide reformulations of the string (super)gravities in which the global duality invariance is made manifest.…”