Gravitational Contributions to Running of Gauge Couplings

Gravitational contributions to the running of gauge couplings are calculated by using different regularization schemes. As the beta function concerns counter-terms of dimension four, only quadratic divergences from the gravitational contributions need to be investigated. A consistent result is obtained by using asymmetry-preserving loop regularization with string-mode regulators which can appropriately treat the quadratic divergences and preserve non-abelian gauge symmetry. The harmonic gauge condition for gravity is used in both diagrammatical and back ground field calculations, the resulting gravitational corrections to the beta function are found to be nonzero, which is different from previous results presented in the existing literatures.