Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge

We study the parametrization and gauge dependences in the Higgs field coupled to gravity in the context of asymptotic safety. We use the exponential parametrization to derive the fixed points for the cosmological constant, Planck mass, Higgs mass and its coupling, keeping arbitrary gauge parameters alpha and beta and compare the results with the linear split. We find that the beta functions for the Higgs potential are expressed in terms of redefined Planck mass such that the apparent gauge dependence is absent. Only the trace mode of the gravity fluctuations couples to the Higgs potential and it tends to decouple in the large beta limit, but the anomalous dimension becomes large, invalidating the local potential approximation. This gives the limitation of the exponential parametrization. There are also singularities for some values of the gauge parameters but well away from these, we find rather stable fixed points and critical exponents. We thus find that there are regions for the gauge parameters to give stable fixed points and critical exponents against the change of gauge parameters. The Higgs coupling is confirmed to be irrelevant for the reasonable choice of gauge parameters.

Automated summary

In this study, we investigate the parametrization and gauge dependences in the Higgs field coupled to gravity in the context of asymptotic safety. By using the exponential parametrization, we derive fixed points for various parameters and compare the results with the linear split. We find that the gauge dependence of the Higgs potential is eliminated by redefining the Planck mass, but the local potential approximation becomes invalid due to large anomalous dimension. Nevertheless, there exist stable fixed points and critical exponents for certain values of the gauge parameters.