Hamiltonian derivation of dual gravitational charges

119

161

We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein’s equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.

“…[108,109]. More relevant to the study of future null infinity is the recent result that tetrad variables give access to non-vanishing dual BMS charges [110][111][112].…”

Section: Tetrad Variablesmentioning

confidence: 99%

The Weyl BMS group and Einstein’s equations

Freidel

Oliveri

Pranzetti

et al. 2021

119

161

“…There we show how the GR charge written as H S ECH [ξ]−H S ECH/GR [ξ] and in the parametrization introduced in section 6 contains two terms. One is a Holst piece which yields the so-called topological Komar charge (see also [115,176]). The second one is a gravitational piece which yields the Brown-York charge expressed in first order variables, as expected for the GR charge [1].…”

Section: Jhep11(2020)027mentioning

confidence: 99%

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Freidel

Geiller

Pranzetti

2020

108

205

In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local $$ \mathfrak{sl} $$ sl (2, ℂ) component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local $$ \mathfrak{sl} $$ sl (2, ℝ) algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.

“…For related works in other formalisms see e.g. [24,[67][68][69][70][71][72][73][74][75][76][77][78][79][80][81]. Note that it is expected that different formalisms lead to different symmetry algebras [77].…”

Section: Introductionmentioning

confidence: 99%

Conservation and integrability in lower-dimensional gravity

Ruzziconi

Zwikel

2021

113

We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.