On the Interpretation of Gravitational Corrections to Gauge Couplings

TL;DR

This paper argues that quadratic gravitational corrections to gauge couplings, often discussed in recent literature, are not physically meaningful as they can be removed by local field redefinitions and do not affect measurable scattering processes.

Contribution

It demonstrates that quadratic gravitational corrections to gauge couplings are non-physical and can be eliminated through local field redefinitions, clarifying their role in string theory and gauge coupling running.

Findings

Quadratic gravitational corrections can be removed by local field redefinitions.

Such corrections do not contribute to physical scattering amplitudes.

They are not relevant for gauge coupling unification or running.

Abstract

Several recent papers discuss gravitational corrections to gauge couplings that depend quadratically on the energy. In the framework of the background-field approach, these correspond in general to adding to the effective action terms quadratic in the field strength but with higher-order space-time derivatives. We observe that such terms can be removed by appropriate local field redefinitions, and do not contribute to physical scattering-matrix elements. We illustrate this observation in the context of open string theory, where the effective action includes, among other terms, the well-known Born-Infeld form of non-linear electrodynamics. We conclude that the quadratically energy-dependent gravitational corrections are \emph{not} physical in the sense of contributing to the running of a physically-measurable gauge coupling, or of unifying couplings as in string theory.