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Abstract
Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order $\alpha'^3$. In this paper we use the cosmological reduction on the couplings and show that, up to field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.
Highlights
A theory of gravity in a spacetime manifold with/without a boundary that is consistent with the rules of quantum mechanics is string theory
This theory includes the finite number of massless modes and the tower of infinite number of massive modes of the string excitations
The genus expansion includes the classical tree level, i.e., Seff þ ∂Seff, a tower of quantum loop-level corrections, and the stringy expansion that is an expansion in terms of higher derivative couplings at each loop level
Summary
A theory of gravity in a spacetime manifold with/without a boundary that is consistent with the rules of quantum mechanics is string theory. After integrating out the massive modes, the T duality should appears as symmetry in the effective actions It has been shown in [6,7] that the dimensional reduction of the classical effective actions of the bosonic and heterotic string theories on a torus Td are invariant under Oðd; d; RÞ transformations. Since the T-duality transformations have higher derivative corrections, the other T-dual multiplets include couplings at all orders of α0. It has been observed in [13]
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