L-algebras of Einstein-Cartan-Palatini gravity

Marija Dimitrijević Ćirić, Grigorios Giotopoulos, Voja Radovanović, Richard J. Szabo

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Abstract

We give a detailed account of the cyclic L∞-algebra formulation of general relativity with a cosmological constant in the Einstein-Cartan-Palatini formalism on spacetimes of arbitrary dimension and signature, which encompasses all symmetries, field equations, and Noether identities of gravity without matter fields. We present a local formulation as well as a global covariant framework, and an explicit isomorphism between the two L∞-algebras in the case of parallelizable spacetimes. By duality, we show that our L∞-algebras describe the complete Batalin-Vilkovisky-Becchi-Rouet-Stora-Tyutin formulation of Einstein-Cartan-Palatini gravity. We give a general description of how to extend on-shell redundant symmetries in topological gauge theories to off-shell correspondences between symmetries in terms of quasi-isomorphisms of L∞-algebras. We use this to extend the on-shell equivalence between gravity and Chern-Simons theory in three dimensions to an explicit L∞-quasi-isomorphism between differential graded Lie algebras, which applies off-shell and for degenerate dynamical metrics. In contrast, we show that there is no morphism between the L∞-algebra underlying gravity and the differential graded Lie algebra governing BF theory in four dimensions.

Original languageEnglish
Article number112502
JournalJournal of Mathematical Physics
Volume61
Issue number11
Early online date6 Nov 2020
DOIs
Publication statusPublished - Nov 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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