Abstract
Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories are free of scalar ghosts. We canonically analyze these theories and construct the gauge generators and the boundary central charges. The models we construct are all consistent with a holographic c-theorem which, however, does not imply that they are unitary. We find that Born-Infeld gravity in three dimensions is contained within these models as a subclass.
Highlights
Gravity is one of the earliest applications of the AdS/CFT correspondence which organizes our understanding of a quantum gravity theory in terms of a dual conformal field theory (CFT) and vice versa
The AdS boundary conditions are presented in terms of some free state dependent normalizable contributions to this background. These contributions behave as the vacuum expectation value (VEV) for the boundary operators which are sourced by non-normalizable modes
We proposed a systematic procedure of constructing higher-derivative extensions of 3D general relativity which are free of scalar ghost degrees of freedom and propagate massive spin-2 excitations
Summary
We give a procedure to derive higher-derivative extensions of 3D GR which propagate multiple massive spin-2 particles. Our starting point is a first order, Chern-Simons-like formalism [11, 12], defined by a Lagrangian three-form depending on the dreibein ea, the dualized spin-connection ωa and a number of new auxiliary Lorentz vector valued one-forms fIa and haI The advantage of this approach is that it automatically leads to higher-derivative terms which are free of scalar ghosts, as we will show below. The other auxiliary form fields (fI , hI ) can be obtained in terms of e and derivatives acting on it, such that the final equation is a higher-derivative field equation for the dreibein This set of equations may terminate with an equation for DhN or DfN+1.
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