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Inequivalence of first- and second-order formulations in D=2 gravity models

Abstract

The usual equivalence between the Palalini and metric (or affinity and vielbein) formulations of Einstein theory fails in two spacetime dimensions for its “Kaluza-Klein” reduced (as well as for its standard) version. Among the differences is the necessary vanishing of the cosmological constant in the first-order forms. The purely affine Eddington formulation of Einstein theory also fails here.

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The present results were reported in the Proceedings of the Markov Memorial Quantum Gravity Seminar.

This work was supported bt the NSF under grant #PHY-9315811.

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Deser, S. Inequivalence of first- and second-order formulations in D=2 gravity models. Found Phys 26, 617–621 (1996). https://doi.org/10.1007/BF02058235

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  • DOI: https://doi.org/10.1007/BF02058235

Keywords

  • Cosmological Constant
  • Gravity Model
  • Spacetime Dimension
  • Einstein Theory