Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry

TL;DR

This paper investigates how UV modifications in various theories, including Lorentz invariant and non-invariant models, affect gravitational parameters and entanglement entropy, revealing sensitivity to UV behavior and conditions for finiteness.

Contribution

It provides a systematic analysis of gravitational effective action and entanglement entropy in UV-modified theories, including non-Lorentz invariant Lifshitz models, using generalized heat kernel methods.

Findings

Induced cosmological constant and gravitational couplings depend on UV modifications.

Extrinsic curvature couplings are UV finite under certain Lifshitz operator conditions.

The heat kernel method is generalized for a broad class of UV-modified theories.

Abstract

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.