Motivated by establishing holographic renormalization for gravitational theories with non-metricity and torsion, we present a new and efficient general method for calculating Gibbons-Hawking-York (GHY) terms. Our method consists of linearizing any nonlinearity in curvature, torsion or non-metricity by introducing suitable Lagrange multipliers. Moreover, we use a split formalism for differential forms, writing them in $(n-1)+1$ dimensions. The boundary terms of the action are manifest in this formalism by means of Stokes' theorem, such that the compensating GHY term for the Dirichlet problem may be read off directly. We observe that only those terms in the Lagrangian that contain curvature contribute to the GHY term. Terms polynomial solely in torsion and non-metricity do not require any GHY term compensation for the variational problem to be well-defined. We test our method by confirming existing results for Einstein-Hilbert and four-dimensional Chern-Simons modified gravity. Moreover, we obtain new results for torsionful Lovelock-Chern-Simons and metric-affine gravity. For all four examples, our new method and results contribute to a new approach towards a systematic hydrodynamic expansion for spin and hypermomentum currents within AdS/CFT.
Cited by 1
Cassani et al., Boundary terms and conserved charges in higher-derivative gauged supergravity
J. High Energ. Phys. 2023, 203 (2023) [Crossref]
Authors / Affiliations: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Julius-Maximilians-Universität Würzburg / University of Würzburg
- 2 Würzburg-Dresden Cluster of Excellence [ct.qmat]
- 3 Università degli Studi di Genova / University of Genoa [UniGe]
- 4 Istituto Nazionale di Fisica Nucleare Sezione di Genova / National Institute of Nuclear Physics Genoa Section [INFN Genova]
- Bundesministerium für Bildung und Forschung / Federal Ministry of Education and Research [BMBF]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
- Universita degli Studi di Genova (UniGe) (through Organization: Università degli Studi di Genova / University of Genoa [UniGe])