Finite gravitational action for higher derivative and stringy gravities

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.

LaTeX file, 21 pages

References in corpus (4)

• Large N Field Theories, String Theory and Gravity
• The Gravitational Action in Asymptotically AdS and Flat Spacetimes
• On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence
• Strong Coupling Limit of $\mathcal{N}=2$ SCFT Free Energy and Higher Derivative AdS/CFT Correspondence

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