Gravitational corrections to a non-Abelian gauge theory

This paper is part of a series of papers exploring the renormalization of field theories coupled to gravity using the effective field theory framework. In previous works, we studied the universality of the electric charge and the two-loops beta function in the Einstein-QED system. Now, we use this framework to study the non-Abelian gauge theory with fermions coupled to gravity. We show that even though some of the counterterms are dependent on the gravitational coupling, the renormalized coupling constant, and therefore the beta function, do not receive any gravitational correction at one-loop order. Also, we explicitly show that, at this order, the Slavnov-Taylor identities are respected. Finally, we end the paper by putting into perspective the results of the present and the past papers.

Figure 1

Feynman diagrams for the quark top self-energy. Continuous, wiggly, dotted, and dashed lines represent the fermion, gluon, ghost, and graviton propagators, respectively. The $t$ label represents the quark-top, since this is the most massive quark and therefore, will have the major gravitational contributions. For the others self-energies, we just have to change the quark-top propagators for the other ones.

Figure 2

Feynman diagrams for the gluon self-energy.

Figure 3

Feynman diagrams for the ghost self-energy.

Figure 4

Feynman diagrams for the vertex interaction between gluons and ghosts up to one-loop order.

Figure 5

Feynman diagrams to the vertex interaction between quarks top and gluons up to one-loop order.

Figure 6

The gray color represents negative charges while the black color represents positive charges. The central circle is an electron surrounded by polarized virtual particles.

Figure 7

Feynman diagrams to the gluons vertex interaction at one-loop order.

Figure 8

Feynman diagrams to the scattering between gluons up to one-loop order.

Figure 9

Feynman diagrams to the gluon self-energy involving gravitons at two-loop order.