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Note about a pure spin-connection formulation of general relativity and spin-2 duality in (A)dS

Thomas Basile1,2,*, Xavier Bekaert1,†, and Nicolas Boulanger2,‡

  • 1Laboratoire de Mathématiques et Physique Théorique Unité Mixte de Recherche du CNRS Fédération de Recherche Denis Poisson Université François Rabelais, Parc de Grandmont 37200 Tours, France
  • 2Groupe de Mécanique et Gravitation Service de Physique Théorique et Mathématique Université de Mons-UMONS, Place du Parc 20, 7000 Mons, Belgique

  • *thomas.basile@umons.ac.be
  • †xavier.bekaert@lmpt.univ-tours.fr
  • ‡Research Associate of the Fund for Scientific Research-FNRS (Belgium); nicolas.boulanger@umons.ac.be
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Phys. Rev. D 93, 124047 – Published 21 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.124047

Abstract

We investigate the problem of finding a pure spin-connection formulation of general relativity with nonvanishing cosmological constant. We first revisit the problem at the linearized level and find that the pure spin-connection, quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by the square of a Weyl-like tensor. Upon Hodge dualization, we show that the dual gauge field in (A)dSD transforms under GL(D) in the same representation as a massive graviton in the flat spacetime of the same dimension. We give a detailed proof that the physical degrees of freedom indeed correspond to a massless graviton propagating around the (anti-) de Sitter background and finally speculate about a possible nonlinear pure-connection theory dual to general relativity with cosmological constant.

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Phys. Rev. D 93, 124047– Published 21 June, 2016
  • Received 29 March 2016

© 2016 American Physical Society

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