Gravitational Contributions to the Running of Gauge Couplings

Gravitational contributions to the running of gauge couplings are calculated by using different regularization schemes. As the $β$ 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 a symmetry-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 background field calculations, the resulting gravitational corrections to the $β$ function are found to be nonzero, which is different from previous results presented in the existing literatures.

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