An official website of the United States government
We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with space–time subregions, as well as global conserved charges of the full space–time. Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries. The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles. In the context of asymptotic boundaries, we show that the procedure of holographic renormalization can be always applied to obtain finite charges and fluxes once suitable counterterms have been found to ensure a finite action. This enables the study of larger asymptotic symmetry groups by loosening the boundary conditions imposed at infinity. We further present an algorithm for explicitly computing the counterterms that renormalize the action and symplectic potential, and, as an application of our framework, demonstrate that it reproduces known expressions for the charges of the generalized Bondi–Metzner–Sachs algebra.
more »
« less
On the charge algebra of causal diamonds in three dimensional gravity
A<sc>bstract</sc> Covariant phase space methods are applied to the analysis of a causal diamond in 2+1-dimensional pure Einstein gravity. It is found that the reduced phase space is parametrized by a family of charges with a dual geometrical interpretation: they are geometric observables on the corner of the diamond, and they generate diffeomorphisms. The Poisson brackets among them close into an algebra. Knowledge of the corner charges therefore permits reconstruction of the diamond geometry, which realizes a form of local holography. The results are contrasted with the literature, and the path to a quantum description of spacetime geometry is discussed.
more »
« less
- PAR ID:
- 10614415
- Publisher / Repository:
- Journal of High Energy Physics
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 7
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A<sc>bstract</sc> We study the entanglement phase structure of a holographic boundary conformal field theory (BCFT) in a two-dimensional black hole background. The bulk dual is the AdS3black string geometry with a Karch-Randall brane. We compute the subregion entanglement entropy of various two-sided bipartitions to elucidate the phase space where a Page curve exists in this setup. We do fully analytical computations on both the gravity side and the field theory side and demonstrate that the results precisely match. We discuss the entanglement phase structure describing where a Page curve exists in this geometry in the context of these analytical results. This is a useful model to study entanglement entropy for quantum field theory on a curved background.more » « less
-
A<sc>bstract</sc> We consider the problem of defining a microcanonical thermofield double state at fixed energy and angular momentum from the gravitational path integral. A semiclassical approximation to this state is obtained by imposing a mixed boundary condition on an initial time surface. We analyze the corresponding boundary value problem and gravitational action. The overlap of this state with the canonical thermofield double state, which is interpreted as the Hartle-Hawking wavefunction of an eternal black hole in a mini-superspace approximation, is calculated semiclassically. The relevant saddlepoint is a higher-dimensional, rotating generalization of the wedge geometry that has been studied in two-dimensional gravity. Along the way we discuss a new corner term in the gravitational action that arises at a rotating horizon.more » « less
-
We derive a prescription for the phase space of general relativity on two intersecting null surfaces using the null initial value formulation. The phase space allows generic smooth initial data, and the corresponding boundary symmetry group is the semidirect product of the group of arbitrary diffeomorphisms of each null boundary which coincide at the corner, with a group of reparameterizations of the null generators. The phase space can be consistently extended by acting with half-sided boosts that generate Weyl shocks along the initial data surfaces. The extended phase space includes the relative boost angle between the null surfaces as part of the initial data. We then apply the Wald-Zoupas framework to compute gravitational charges and fluxes associated with the boundary symmetries. The non-uniqueness in the charges can be reduced to two free parameters by imposing covariance and invariance under rescalings of the null normals. We show that the Wald-Zoupas stationarity criterion cannot be used to eliminate the non-uniqueness. The different choices of parameters correspond to different choices of polarization on the phase space. We also derive the symmetry groups and charges for two subspaces of the phase space, the first obtained by fixing the direction of the normal vectors, and the second by fixing the direction and normalization of the normal vectors. The second symmetry group consists of Carrollian diffeomorphisms on the two boundaries. Finally we specialize to future event horizons by imposing the condition that the area element be non-decreasing and become constant at late times. For perturbations about stationary backgrounds we determine the independent dynamical degrees of freedom by solving the constraint equations along the horizons. We mod out by the degeneracy directions of the presymplectic form, and apply a similar procedure for weak non-degeneracies, to obtain the horizon edge modes and the Poisson structure. We show that the area operator of the black hole generates a shift in the relative boost angle under the Poisson bracket.more » « less
-
A<sc>bstract</sc> Finding string backgrounds with de Sitter spacetime, where all approximations and corrections are controlled, is an open problem. We revisit the search for de Sitter solutions in the classical regime for specific type IIB supergravity compactifications on group manifolds, an under-explored corner of the landscape that offers an interesting testing ground for swampland conjectures. While the supergravity de Sitter solutions we obtain numerically are ambiguous in terms of their classicality, we find an analytic scaling that makes four out of six compactification radii, as well as the overall volume, arbitrarily large. This potentially provides parametric control over corrections. If we could show that these solutions, or others to be found, are fully classical, they would constitute a counterexample to conjectures stating that asymptotic de Sitter solutions do not exist. We discuss this point in great detail.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP07(2024)251
