Einsteinian gravity from BRST quantization of a topological action

Eckehard W. Mielke
Phys. Rev. D 77, 084020 – Published 28 April 2008; Erratum Phys. Rev. D 77, 109902 (2008)

Abstract

In order to deduce Einsteinian gravity from a topological action, we start from the metric-free Pontrjagin invariant in four dimensions. Using the Becchi-Rouet-Stora-Tyutin antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature. They correspond to classical instanton type solutions of a curvature-squared model of gravity, in the affine form proposed already by Weyl and Yang. However, the exact vacuum solutions with double duality properties exhibit a “vacuum degeneracy.” By modifying the duality of the curvature via scale breaking terms, we demonstrate that only Einstein’s equations with an induced cosmological constant of partially topological origin emerge for the macroscopic “background.”

  • Received 31 May 2007
  • Publisher error corrected 29 April 2008

DOI:https://doi.org/10.1103/PhysRevD.77.084020

©2008 American Physical Society

Corrections

29 April 2008

Erratum

Authors & Affiliations

Eckehard W. Mielke*

  • Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, P.O. Box 55-534, 09340 México D.F., México

  • *ekke@xanum.uam.mx

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Issue

Vol. 77, Iss. 8 — 15 April 2008

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