Abstract
We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order α^{'}^{3}, with an overall coefficient proportional to ζ(3), and show that it is compatible with an O(9,9) symmetry. This confirms the general result in string theory, due to Sen [O(d)×O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271, 295 (1991)PYLBAJ0370-269310.1016/0370-2693(91)90090-D], that classical string theory with d-dimensional translation invariance admits an O(d,d) symmetry to all orders in α^{'}.
Highlights
Introduction.—String theory continues to be a most promising framework for a consistent theory of quantum gravity
We compute the cosmological reduction of the fourth powers of the Riemann tensor claimed to arise in string theory at order α03, with an overall coefficient proportional to ζð3Þ, and show that it is compatible with an Oð9; 9Þ symmetry
This confirms the general result in string theory, due to Sen [OðdÞ × OðdÞ symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys
Summary
As shown by Sen [17], classical (tree-level) string theory truncated to states of zero momentum along d directions admits an Oðd; d; RÞ invariance to all orders in α0 [17]. The tree-level corrections at order α03 proportional to ζð3Þ really ought to be consistent with Oðd; d; RÞ, and they are. The couplings for the gravitational sector were originally computed from fourpoint scattering amplitudes [1] and later from the sigmamodel β function [19,20,21]. The first term in Eq (1) is t8t8R4 1⁄4 t tRRRR μ1...μ8 ν1...ν8 μ1μ2 ν1ν2 μ3μ4 ν3ν4 μ5μ6 ν5ν6 μ7μ8 ν7ν8
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