On factorizations in perturbative quantum gravity

TL;DR

This paper develops a framework for Einstein gravity coupled to matter fields where T-duality ensures all-order factorization of Feynman rules, clarifying the relation between different formulations and making left-right factorization explicit.

Contribution

It introduces a perturbative Einstein gravity framework with manifest factorization using double field theory and a geometrical formalism, linking various field variables.

Findings

Feynman rules factorize to all orders in perturbation theory.

Established the relation between different field formulations.

Presented a Lagrangian with explicit left-right factorization.

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.