Abstract
We address some issues in higher-derivative gauged supergravity with Chern-Simons terms, focusing on the five-dimensional case. We discuss the variational problem with Dirichlet boundary conditions as well as holographic renormalization in asymptotically locally AdS spacetimes, and derive the corresponding boundary terms. We then employ Wald’s formalism in order to define conserved charges associated to local symmetries (diffeomorphisms and U(1) gauge transformations), taking into account the effect of generic gauge Chern-Simons terms. We prove that the first law of black hole mechanics and the quantum statistical relation hold in this setup. Chern-Simons terms also lead us to distinguish between Noether charges and Page (or Komar) charges which satisfy the Gauss law. We make use of the latter to compute corrections to the angular momentum and electric charge of the supersymmetric black hole in AdS5 from its corrected near-horizon geometry. This also allows us to derive the microcanonical form of the entropy as a function of the conserved charges relying entirely on the near-horizon geometry. Finally, we comment on four-derivative gauged supergravity in four dimensions, showing that field redefinitions permit to simplify the action at linear order in the corrections, so that the equations of motion are those of the two-derivative theory.
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Acknowledgments
We are grateful to Pablo A. Cano, Tomás Ortín, David Pereñiguez and Dan Waldram for useful discussions. AR thanks the University of Padova and the INFN Sezione di Padova for hospitality and financial support during the final stages of this work. AR is supported by a postdoctoral fellowship associated to the MIUR-PRIN contract 2020KR4KN2, “String Theory as a bridge between Gauge Theories and Quantum Gravity”.
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Cassani, D., Ruipérez, A. & Turetta, E. Boundary terms and conserved charges in higher-derivative gauged supergravity. J. High Energ. Phys. 2023, 203 (2023). https://doi.org/10.1007/JHEP06(2023)203
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DOI: https://doi.org/10.1007/JHEP06(2023)203