A note on dual gravitational charges

We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two restricting hypothesis. In particular, we derive the general field-dependent gauge transformations of the presymplectic potential and presymplectic 2-form in both cases. We point-out that a generalisation of the standard bundle geometry, called twisted geometry, arises naturally in the study of non-invariant gauge theories (e.g. non-Abelian Chern-Simons theory). These results prove that the well-known problem of associating a symplectic structure to a gauge theory over bounded regions is a generic feature of both classes. The edge modes strategy, recently introduced to address this issue, has been actively developed in various contexts by several authors. We draw attention to the dressing field method as the geometric framework underpinning, or rather encompassing, this strategy. The geometric insight afforded by the method both clarifies it and clearly delineates its potential shortcomings as well as its conditions of success. Applying our general framework to various examples allows to straightforwardly recover several results of the recent literature on edge modes and on the presymplectic structure of general relativity.

Section: Jhep03(2021)225supporting

confidence: 90%

Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method

François

2021

“…[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 differences show up for instance in the formulas for the quasi-local charges, which been investigated in [81,113] and [38][39][40]; see also [107,[114][115][116][117] for previous related work. It is known that equivalence of the charges can be restored for isometries using the Kosmann derivative [114][115][116] (see discussion in [81]), but for asymptotic symmetries is it not always the case [111,112]: at null infinity the standard charges are the same but not the dual ones, thus offering a set-up to recover known BMS results, while at the same time accessing the dual sector. The exact equivalence can be obtained for all charges including arbitrary diffeomorphisms if one works with a dressed symplectic potential [81,113] (see also [87,118]).…”

Section: Tetrad Variablesmentioning

confidence: 99%

The Weyl BMS group and Einstein’s equations

Freidel

Oliveri

Pranzetti

et al. 2021

Self Cite

104

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.

“…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.