Second order higher-derivative corrections in Double Field Theory

Abstract

HSZ Double Field Theory is a higher-derivative theory of gravity with exact and manifest T-duality symmetry. The first order corrections in the massless sector were shown to be governed solely by Chern-Simons deformations of the three-form field strength. We compute the full action with up to six derivatives O(α ′2 ) for the universal sector containing the metric, two-form and dilaton fields. The Green-Schwarz transformation of the two-form field remains uncorrected to second order. In addition to the expected ChernSimons-squared and Riemann-cubed terms the theory contains a cubic Gauss-Bonnet interaction, plus other six-derivative unambiguous terms involving the three-form field strength whose presence indicates that the theory must contain further higher-derivative corrections.

The generalized Bergshoeff-de Roo identification

“…A similar question has been addressed is the HSZ setup [11]. Both frameworks are similar in that there is a closed non-perturbative form of the gauge transformations and action, which can then be perturbed in a derivative expansion (see [36], [37], [38], [39], [40]), such that when written in terms of an O(D, D) generalized frame or metric acquires infinite α ′ corrections. It is certainly desirable to learn what kind of information can be extracted from these closed and exact expressions.…”

T-duality equivalences beyond string theory

“…It would also be interesting to explore whether our results hold for higher orders in the derivative expansion. Building these actions seems a quite difficult challenge, albeit substantial progress has been achieved recently [29,30].…”

T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm

“…In order to have a better understanding, one would need to explore the generalization of these results to O(γ 2 ± ). The action becomes rather intractable, as explicitly shown in [42] for the case γ + = γ − , which was originally considered by Hohm, Siegel and Zwiebach [20].…”