Abstract
We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. Using this new renormalization prescription, we directly find the C−function candidates for odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.
Highlights
Higher curvature terms likewise enrich our understanding of holography
We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity
By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for asymptotically AdS (AAdS) spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional
Summary
Lovelock gravity is the most general pure gravity action such that it has second order differential equations for the dynamical variable, i.e., the metric [36]. The Lovelock theories we shall consider are higher-curvature corrections to Einstein-AdS gravity and unless otherwise stated, the values of α0 and α1 are always given as in eq (2.3). It is easy to see that the roots obtained from eq (2.8) may have algebraic multiplicity higher than one, which in turn implies that the vacua of the corresponding Lovelock theory are degenerate. D 2 is the order (in powers of the Riemann curvature) of the Lovelock Lagrangian and eff(i) are the effective AdS radii of the theory, given by the solutions of the characteristic polynomial of eq (2.8) [54]. In the case of even-dimensional bulks, a useful rewriting of the renormalized action in terms of a polynomial on the AdS curvature of the manifold is obtained, which is a generalization of the renormalized volume formula proposed for Einstein-AdS [43]
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