Second order higher-derivative corrections in Double Field Theory

TL;DR

This paper computes second-order higher-derivative corrections in HSZ Double Field Theory, revealing new interactions and confirming the structure of T-duality invariant gravity with six-derivative terms.

Contribution

It provides the full second-order (up to six derivatives) action for the universal sector in HSZ Double Field Theory, including new higher-derivative interactions.

Findings

Presence of a cubic Gauss-Bonnet term

Uncorrected Green-Schwarz transformation at second order

Additional six-derivative terms involving the three-form field strength

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 ${\cal O} (\alpha'{}^2)$ 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 Chern-Simons-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.