On factorizations in perturbative quantum gravity

TL;DR

This paper shows that perturbative Einstein gravity coupled to a 2-form and a dilaton admits a Lagrangian in which left-right factorization is manifest due to T-duality. By employing double field theory with $O(D,D)$ invariance and Siegel’s frame formalism, the string-field-theory variable $e_{ij}$ is identified with a frame fluctuation, making the left-right contractions automatic and preserving factorization to all orders. The work provides explicit transformations and perturbative expansions in a frame-like setting, connecting conventional Einstein variables, string-theory variables, and frame variables. These results lay groundwork toward making KLT-type relations more transparent in the Lagrangian framework and suggest geometric avenues for understanding string field theory within gravity.

Abstract

Some features of Einstein gravity are most easily understood from string theory but are not manifest at the level of the usual Lagrangian formulation. One example is the factorization of gravity amplitudes into gauge theory amplitudes. Based on the recently constructed `double field theory' and a geometrical frame-like formalism developed by Siegel, we provide a framework of perturbative Einstein gravity coupled to a 2-form and a dilaton in which, as a consequence of T-duality, the Feynman rules factorize to all orders in perturbation theory. We thereby establish the precise relation between the field variables in different formulations and discuss the Lagrangian that, when written in terms of these variables, makes a left-right factorization manifest.