A Note on Gauge Systems from the Point of View of Lie Algebroids

Barnich, Glenn

doi:10.1063/1.3527427

Cited by 38 publications

(62 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the same way than the modified Lie bracket needed to represent the asymptotic symmetry algebra in the bulk space-time is the bracket of the Lie algebroid naturally associated to gauge systems [27], field dependent central extensions correspond to Liealgebroid 2-cocycles rather than to Lie algebra 2-cocycles. Note that, besides the standard central extensions in the two Witt subalgebras, the bms 4 algebra does not admit additional non trivial central extensions involving the supertranslation generators, i.e., there are no additional non trivial Lie algebra 2-cocycles with values in the real numbers (see e.g.…”

Section: Discussionmentioning

confidence: 99%

BMS charge algebra

Barnich

Troessaert

2011

J. High Energ. Phys.

430

745

View full text Add to dashboard Cite

ABSTRACT. The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslations charges diverge whereas there are no divergences for the superrotation charges. The central extension is proportional to the rotation parameter and involves divergent integrals on the sphere.

show abstract

Section: Discussionmentioning

confidence: 99%

BMS charge algebra

Barnich

Troessaert

2011

J. High Energ. Phys.

430

745

View full text Add to dashboard Cite

show abstract

“…A novel result in our study concerns the realization of the asymptotic algebra not only on the boundary Scri but in the bulk gauge fixed spacetime by using a natural modification of the Lie bracket for vector fields that depend on the metric and is related to the theory of Lie algebroids [19]. Furthermore, this modified bracket is also needed for the realization on Scri in order to disentangle the gauge transformations from the residual global symmetries when allowing for changes of the conformal factor.…”

Section: Asymptotic Versus Complete Gauge Fixations Realizationsmentioning

confidence: 99%

Aspects of the BMS/CFT correspondence

Barnich¹,

Troessaert²

2011

Proceedings of Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravit

143

269

View full text Add to dashboard Cite

We review recent results on symmetries of asymptotically flat spacetimes at null infinity. In higher dimensions, the symmetry algebra realizes the Poincaré algebra. In three and four dimensions, besides the infinitesimal supertranslations that have been known since the sixties, the algebras are evenly balanced because there are also infinitesimal superrotations. We provide the classification of central extensions of bms 3 and bms 4 . Applications and consequences as well as directions for future work are briefly indicated.

show abstract

“…The bulk symmetry parameter (2.2) is field dependent (through the metric function J ) and therefore its algebra is given by the modified bracket [25,26] […”

Section: Jhep03(2015)158mentioning

confidence: 99%

Liouville theory beyond the cosmological horizon

Compère

Donnay

Lambert

et al. 2015

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk.

show abstract

A Note on Gauge Systems from the Point of View of Lie Algebroids

Abstract: ABSTRACT. In the context of the variational bi-complex, we re-explain that irreducible gauge systems define a particular example of a Lie algebroid. This is used to review some recent and not so recent results on gauge, global and asymptotic symmetries.

Cited by 38 publications

References 26 publications

BMS charge algebra

BMS charge algebra

Aspects of the BMS/CFT correspondence

Liouville theory beyond the cosmological horizon

Contact Info

Product

Resources

About