A note on the dimensional regularization of the Standard Model coupled with Quantum Gravity

TL;DR

This paper addresses the challenge of maintaining Lorentz invariance in dimensional regularization of the Standard Model coupled with quantum gravity, proposing a deformation of the Einstein Lagrangian to simplify Feynman diagram calculations.

Contribution

It introduces a method to deform the Einstein Lagrangian and gauge-fix residual local Lorentz symmetry, ensuring Lorentz invariant denominators in propagators for quantum gravity coupled with the Standard Model.

Findings

Propagators have fully Lorentz invariant denominators.

Simplifies Feynman diagram calculations in quantum gravity models.

Addresses gamma5 and epsilon tensor issues in dimensional regularization.

Abstract

In flat space, gamma5 and the epsilon tensor break the dimensionally continued Lorentz symmetry, but propagators have fully Lorentz invariant denominators. When the Standard Model is coupled with quantum gravity gamma5 breaks the continued local Lorentz symmetry. I show how to deform the Einstein lagrangian and gauge-fix the residual local Lorentz symmetry so that the propagators of the graviton, the ghosts and the BRST auxiliary fields have fully Lorentz invariant denominators. This makes the calculation of Feynman diagrams more efficient.