3D Born-Infeld gravity and supersymmetry

  • Eric Bergshoeff
  • Mehmet Ozkan
Open Access


We construct the most general parity-even higher-derivative \( \mathcal{N} \) = 1 off-shell supergravity model in three dimensions with a maximum of six derivatives. Excluding terms quadratic in the curvature tensor with two explicit derivatives and requiring the absence of ghosts in a linearized approximation around an AdS3 background, we find that there is a unique supersymmetric invariant which we call supersymmetric ‘cubic extended’ New Massive Gravity. The purely gravitational part of this invariant is in agreement with an earlier analysis based upon the holographic c-theorem and coincides with an expansion of Born-Infeld gravity to the required order.

Our results lead us to propose an expression for the bosonic part of off-shell \( \mathcal{N} \) = 1 Born-Infeld supergravity in three dimensions that is free of ghosts. We show that different truncations of a perturbative expansion of this expression gives rise to the bosonic part of (i) Einstein supergravity; (ii) supersymmetric New Massive Gravity and (iii) supersymmetric ‘cubic extended’ New Massive Gravity.


Classical Theories of Gravity Supergravity Models 


Open Access

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© The Author(s) 2014

Authors and Affiliations

  1. 1.Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands

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