Abstract
We compute the cosmological reduction of general string theories, including bosonic, heterotic, and type II string theory to order ${\ensuremath{\alpha}}^{\ensuremath{'}3}$, i.e., with up to eight derivatives. To this end, we refine recently introduced methods that allow one to bring the reduced theory in one dimension to a canonical form with only first-order time derivatives. The resulting theories are compatible with a continuous $O(d,d,\mathbb{R})$ invariance, which in turn fixes the B-field couplings.
Highlights
One of the fascinating features of string theory is its invariance under dualities that, in the simplest case, send the metric g to its inverse g−1
One reason is that even classical string theory restricted to the massless fields contains an infinite number of higher-derivative α0 corrections which contribute to the cosmological equations, and only very little is known about these corrections. (See [7] for applications of higher derivative corrections in string cosmology.) In this paper, which is a continuation of our recent letter [8], we determine the cosmological reduction for all string theories up to and including α03 for metric, B field, and dilaton
In [8], we showed that the α03 corrections involving the eight-derivative couplings known as t8t8R4 and ε10ε10R4 need to arise with a specific relative coefficient in order to be compatible with Oðd; dÞ, which turns out to be the coefficient previously determined by other methods [19]
Summary
One of the fascinating features of string theory is its invariance under dualities that, in the simplest case, send the metric g to its inverse g−1. Our analysis is made possible by the results of [9,10], which classify the α0 corrections in one dimension (cosmic time) up to field redefinitions This leads to a drastic reduction of the number of possible terms arising in the one-dimensional action. We find it instructive to give this result in an alternative form, in terms of three parameters ða; b; cÞ that encode the α0 corrections of all string theories. Coefficients of the cosmological classification for different strings This parametrization of the action is motivated by double field theory [a reformulation of the target space theory that is Oðd; dÞ covariant before dimensional reduction], which permits a 2-parameter α0 deformation [15,16] that is invariant under the Z2 that exchanges the two parameters a, b and simultaneously sends the Oðd; dÞ metric η to −η.
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