Finite gravitational action for higher derivative and stringy gravities

TL;DR

This paper develops a method to regularize the gravitational action in higher derivative and string-inspired gravities, enabling finite actions and well-defined energy-momentum tensors in asymptotically AdS spaces, with applications to holography.

Contribution

It introduces explicit surface counterterms for higher derivative gravities in three and five dimensions, extending the holographic renormalization procedure beyond Einstein gravity.

Findings

Finite gravitational action achieved for HD gravities.

Holographic trace anomalies computed for d2 and d4 boundaries.

AdS black hole masses calculated within the new prescription.

Abstract

We generalize the local surface counterterm prescription suggested in Einstein gravity for higher derivative (HD) and Weyl gravities. Explicitly, the surface counterterm is found for three- and five-dimensional HD gravities. As a result, the gravitational action for asymptotically AdS spaces is finite and gravitational energy-momentum tensor is well-defined. The holographic trace anomaly for d2 and d4 boundary (gauge) QFT dual to above HD gravity is calculated from gravitational energy-momentum tensor. The calculation of AdS black hole mass in HD gravity is presented within above prescrition. The comparison with the standard prescription (using reference spacetime) is done.