Higher-Derivative Corrections via the Double Copy Procedure

TL;DR

This work links higher-derivative gauge theories to duality-invariant gravity via the off-shell Double Copy, introducing a Higher-Derivative Double Theory (HDDT) whose quadratic sector reproduces Weyl gravity plus $b$-field and dilaton contributions. It shows the extraneous $b$-field and dilaton terms are removable by field redefinitions, isolating the Weyl gravity content, and then uplifts HDDT to a DFT$+$ framework that encodes α′-corrections in a doubled geometry. The DFT$+$ construction, when parametrized and subjected to the strong constraint, reproduces the bosonic string’s α′ corrections and yields a consistent DC map to Weyl gravity in the pure gravitational limit. The results establish HDDT as the gravitational side of a DC map involving higher-derivative gauge theories and open avenues to systematically derive α′-corrected Lagrangians, including potential extensions to CDFT and single/zeroth copies. Overall, the paper strengthens the connection between color–kinematics duality and duality-invariant gravitational theories, proposing a concrete route to higher-curvature corrections within the DC framework.

Abstract

Recent advances in the off-shell formulation of the Double Copy (DC) procedure have revealed a profound connection between gauge theories and T-duality invariant frameworks. The main example is Double Field Theory (DFT), emerging as the the off-shell DC of Yang-Mills theory up to cubic order in perturbations. Extending this procedure to a higher-derivative gauge theory gives rise to a Higher-Derivative Double Theory (HDDT), which incorporates Weyl gravity along with $b$-field and dilaton contributions, all in a T-duality invariant manner. In this work, we show that the quadratic contributions of HDDT are directly related (up to field redefinitions) to DFT+, a T-duality invariant model associated with the bosonic string that incorporates first-order $α'$ corrections upon parameterization. Our results expand the potential applications of the off-shell DC program towards constructing perturbative $α'$-corrected Lagrangians, while also opening up possibilities for reversing the map by considering the single and zeroth copies.