Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

Abstract

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 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.

Submission to SciPost, 22+9 pages, v2: extended discussion in section 3.3, added citations

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• The fate of boundary terms in dimensional reductions
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Boundary terms, branes and AdS/BCFT in first-order gravity
• Higher-order gravity models: corrections up to cubic curvature invariants and inflation
• The role of torsion in holographic conductivity
• Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations
• Thermal response of the Nieh-Yan term