Yang-Mills vacuum structure and quantum gravity

TL;DR

This paper investigates how curvature influences the vacuum structure in Yang-Mills theory and explores the impact of quantum metric fluctuations within a renormalizable $R^2$ gravity framework, revealing potential phase transitions.

Contribution

It introduces a renormalization group approach to analyze the effective Lagrangian for gauge fields in curved spacetime and examines quantum gravity effects on vacuum stability.

Findings

Curvature can induce phase transitions between different vacua.

Quantum fluctuations of the metric affect the critical curvature.

The critical curvature depends on gravitational coupling constants.

Abstract

Using renormalization group methods we calculate the derivative expansion of the effective Lagrangian for a covariantly constant gauge field in curved spacetime. Curvature affects the vacuum, in particular it could induce phase transitions between different vacua. We also consider the effect of quantum fluctuations of the metric , in the context of a renormalizable $R^2$ theory. In this case the critical curvature depends on the gravi tational coupling constants.