Finite gravitational action for higher derivative and stringy gravities

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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 the gravitational energy-momentum tensor is well defined. The holographic trace anomaly for 2D and 4D boundary (gauge) QFT dual to the above HD gravity is calculated from the gravitational energy-momentum tensor. The calculation of the AdS black hole mass in HD gravity is presented with the above prescription. A comparison with the standard prescription (using reference spacetime) is done.
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