Abstract
We construct the most general parity-even higher-derivative 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 AdS_3 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 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.
Highlights
The supersymmetric extension of NMG was given in [10, 11]
We find that the supersymmetric completion of these terms contains 8 parameters corresponding to the 8 supersymmetric invariants that we will construct in this work
Setting a1 = 1 we find the following unique solution: a2. Substituting these values into the action (5.1), we find that the terms of mass dimension 6 in the supersymmetric cubic extended new massive gravity model, shortly called the SCNMG model, are given by e−1L(S6C)NMG
Summary
In this subsection we construct a Poincare supergravity theory, together with a cosmological constant, using the superconformal ingredients given in the previous subsection. Using the kinetic multiplet and the (inverse) multiplication rules, it is not difficult to obtain the Lagrangian for a scalar multiplet with conformal weight ω coupled to a compensating multiplet with components φ , λ , S , see. The fermionic terms can be read off from the composite formulae (2.12) With these general multiplication and kinetic multiplet construction rules in hand, it is relative straightforward to construct matter coupled N = 1 Poincare supergravity models. Using these expressions into the action formula (2.9), and gauge fixing via (2.17) and scaling the resulting Lagrangian with factor of −2, we obtain the following supersymmetric cosmological constant Lagrangian (including the fermionic terms) e−1LC. This finishes our review of the construction of Poincare supergravity with a cosmological constant via superconformal methods
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