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Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry. (English) Zbl 1207.81091

Summary: We calculate parameters in the low energy gravitational effective action and the entanglement entropy in a wide class of theories characterized by improved ultraviolet (UV) behavior. These include (i) local and non-local Lorentz invariant theories in which inverse propagator is modified by higher-derivative terms and (ii) theories described by non-Lorentz invariant Lifshitz type field operators. We demonstrate that the induced cosmological constant, gravitational couplings and the entropy are sensitive to the way the theory is modified in UV. For non-Lorentz invariant theories the induced gravitational effective action is of the Horava-Lifshitz type. We show that under certain conditions imposed on the dimension of the Lifshitz operator the couplings of the extrinsic curvature terms in the effective action are UV finite. Throughout the paper we systematically exploit the heat kernel method appropriately generalized for the class of theories under consideration.

MSC:

81T20 Quantum field theory on curved space or space-time backgrounds
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C47 Methods of quantum field theory in general relativity and gravitational theory
81P40 Quantum coherence, entanglement, quantum correlations
94A17 Measures of information, entropy
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