Gauge-invariant quantum gravity corrections to Callan-Symanzik beta functions via the Vilkovisky-DeWitt method and gravity-assisted gauge unification

Gravity is the weakest force in nature, and the gravitational interactions with all standard model (SM) particles can be well described by perturbative expansions of the Einstein-Hilbert action as an effective theory, all the way up to energies below the fundamental Planck scale. We use the Vilkovisky-DeWitt method to derive the first gauge-invariant nonzero gravitational power-law corrections to the Callan-Symanzik beta functions which make both Abel and non-Abel gauge interactions asymptotically free. We further demonstrate that the graviton-induced universal power-law runnings always assist the three SM gauge forces to reach unification around the Planck scale, irrespective of the detail of logarithmic corrections. We further compute the power-law corrections to the SM Higgs sector and derive modified triviality bound on the Higgs boson mass.

Figure 1

Coordinates difference in field space as a manifold.

Figure 2

Graviton-induced radiative corrections to photon self-energy, where wavy external (internal) lines stand for background (fluctuating) photon fields, double lines for gravitons, dotted line for photon ghosts [in Fig. 2e], and circle-dotted lines for graviton ghosts [in Figs. 2d, 2e].

Figure 3

Gravity-assisted gauge unifications in the SM [plot (a)] and in the MSSM [plot (b)]. In each case, the graviton-induced universal power-law runnings become dominant above ${10}^{18}\mathrm{GeV}$ and always drive three gauge couplings to rapidly converge towards the UV fixed point, near the Planck scale.

Figure 4

Graviton-induced self-energy for the scalar field. The dashed lines are fluctuating the scalar field; the double wavy lines denote the graviton; and the line of circles depicts the graviton ghost.

Figure 5

Graviton-induced corrections to the quartic scalar vertex. The dashed lines are the fluctuating scalar field; the double wavy lines denote the graviton; and the line of circles depicts the graviton ghost.

Figure 6

Gravitational power-law corrections to the triviality bound on the SM Higgs boson mass $m_H$, where the region above each curve is excluded. The lower [red] curve includes the graviton-induced corrections and the upper [blue] curve depicts the bound with SM interactions alone.