Unraveling the generalized Bergshoeff-de Roo identification

TL;DR

This paper revisits the generalized Bergshoeff-de Roo identification, providing a geometric interpretation of higher-derivative string corrections using the ext{PS} construction within generalized geometry.

Contribution

It offers a geometric understanding of the gBdR identification's higher-derivative corrections through the ext{PS} construction, linking symmetry-based results to geometric structures.

Findings

Reproduces all corrections at leading and sub-leading order from symmetry considerations.

Provides a geometric interpretation of higher-derivative corrections.

Connects the gBdR identification with generalized geometry via the ext{PS} construction.

Abstract

We revisit duality-covariant higher-derivative corrections which arise from the generalized Bergshoeff-de Roo (gBdR) identification, a prescription that gives rise to a two parameter family of $\alpha'$-corrections to the low-energy effective action of the bosonic and the heterotic string. Although it is able to reproduce all corrections at the leading and sub-leading ($\alpha'^2$) order purely from symmetry considerations, a geometric interpretation, like for the two-derivative action and its gauge transformation is lacking. To address this issue and to pave the way for the future exploration of higher-derivative (=higher-loop for the $\beta$-functions of the underlying $\sigma$-model) corrections to generalized dualities, consistent truncations and integrable $\sigma$-models, we recover the gBdR identification's results from the \PS{} construction that provides a natural notion of torsion and curvature in generalized geometry.