Nonlinearly ghostfree higher curvature gravity
Abstract
We find unitary and local theories of higher curvature gravity in the vielbein formalism, known as Poincaré gauge theory, by utilizing the equivalence to ghostfree massive bigravity. We especially focus on three and four dimensions, but extensions into a higherdimensional spacetime are straightforward. In three dimensions, quadratic gravity L =R +T^{2}+R^{2}, where R is the curvature and T is the torsion with indices omitted, is shown to be equivalent to zweidreibein gravity and free from the ghost at fully nonlinear orders. In a special limit, new massive gravity is recovered. When the model is applied to the AdS /CFT correspondence, unitarity both in the bulk theory and in the boundary theory implies that the torsion must not vanish. On the other hand, in four dimensions, the absence of a ghost at nonlinear order requires an infinite number of higher curvature terms, and these terms can be given by a schematic form R (1 +R /α m^{2})^{1}R , where m is the mass of the massive spin2 mode originating from the higher curvature terms and α is an additional parameter that determines the amplitude of the torsion. We also provide another fourdimensional ghostfree higher curvature theory that contains a massive spin0 mode as well as a massive spin2 mode.
 Publication:

Physical Review D
 Pub Date:
 December 2020
 DOI:
 10.1103/PhysRevD.102.124049
 arXiv:
 arXiv:2009.11739
 Bibcode:
 2020PhRvD.102l4049A
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 14 pages, no figure, published version