Gravitational Contributions to Gauge Green's Functions and Asymptotic Free Power-Law Running of Gauge Coupling

TL;DR

This paper calculates gravitational effects on gauge Green's functions at one-loop, showing they preserve gauge identities and lead to a power-law running of gauge coupling near the Planck scale, using multiple regularization approaches.

Contribution

It provides the first diagrammatic proof that gravitational effects preserve Slavnov-Taylor identities at one-loop and demonstrates a consistent regularization scheme independent calculation.

Findings

Gravitational contributions preserve gauge symmetry identities.

Gauge coupling exhibits asymptotic free power-law running near Planck scale.

Regularization methods yield consistent results across approaches.

Abstract

We perform an explicit one-loop calculation for the gravitational contributions to the two-, three- and four-point gauge Green's functions with paying attention to the quadratic divergences. It is shown for the first time in the diagrammatic calculation that the Slavnov-Taylor identities are preserved even if the quantum graviton effects are included at one-loop level, such a conclusion is independent of the choice of regularization schemes. We also present a regularization scheme independent calculation based on the gauge condition independent background field framework of Vilkovisky-DeWitt's effective action with focusing on both the quadratic divergence and quartic divergence that is not discussed before. With the harmonic gauge condition, the results computed by using the traditional background field method can consistently be recovered from the Vilkovisky-DeWitt's effective action approach by simply taking a limiting case, and are found to be the same as the ones yielded by the diagrammatic calculation. As a consequence, in all the calculations, the symmetry-preserving and divergent-behavior-preserving loop regularization method can consistently lead to a nontrivial gravitational contribution to the gauge coupling constant with an asymptotic free power-law running at one loop near the Planck scale.