Non-minimal coupling, boundary terms and renormalization of the Einstein-Hilbert action

Abstract

A consistent variational procedure applied to the gravitational action requires according to Gibbons and Hawking a certain balance between the volume and boundary parts of the action. We consider the problem of preserving this balance in the quantum effective action for the matter non-minimally coupled to metric. It is shown that one has to add a special boundary term to the matter action analogous to the Gibbons-Hawking one. This boundary term modifies the one-loop quantum corrections to give a correct balance for the effective action as well. This means that the boundary UV divergences do not require independent renormalization and are automatically renormalized simultaneously with their volume part. This result is derived for arbitrary non-minimally coupled matter. The example of 2D Maxwell field is considered in much detail. The relevance of the results obtained to the problem of the renormalization of the black hole entropy is discussed.

14 pages, latex. More discussion added, the case of 2D Maxwell field considered in more details

References in corpus (6)

• Black Hole Entropy and Entropy of Entanglement
• Black Hole Entropy without Brick Walls
• Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant
• One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
• Black Hole Entropy and the Hamiltonian Formulation of Diffeomorphism Invariant Theories
• The one-loop form factors in the effective action, and production of coherent gravitons from the vacuum

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