Unitary Truncations and Critical Gravity: a Toy Model

On unitary subsectors of polycritical gravities

“…By contrast, the theory becomes trivial for even rank; the surviving mode has zero energy. This confirms a conjecture of [21]. An alternative description of this truncation can be given by defining a hierarchy of (conserved) charges and then restricting to a superselection sector in this charge hierarchy.…”

“…In this section, we discuss possible unitary truncations of the polycritical theory at the linearized level. As anticipated in [21] we will find a difference between odd and even rank.…”

“…Another reason for studying polycritical models is provided by the AdS/CFT correspondence where one would expect a non-unitary logarithmic CFT as the dual of a polycritical gravity theory [8,20,21] (see also [22,23]). The non-unitarity of the logarithmic CFT is related to the fact that the Hamiltonian cannot be diagonalized on the fields; there is a Jordan structure [24,25].…”

“…The non-unitarity of the logarithmic CFT is related to the fact that the Hamiltonian cannot be diagonalized on the fields; there is a Jordan structure [24,25]. However, the precise structure of the two-point correlation functions suggests the existence of unitary truncations, and by AdS/CFT also in the gravity theory [21]. The example of six-derivative gravity in d = 3 was treated recently in [26] whereas fourderivative critical gravity in d = 4 appeared in [27].…”

Polycritical Gravities

“…Namely, at the critical point the energy of the massless graviton modes vanishes, together with the mass of the Schwarzschild black hole. It was recently argued from a CFT perspective [10] that this is essentially due to the fact that critical gravity is of rank two (with the rank being half the number of maximum derivatives). Instead, gravity theories of odd rank should not suffer from this 'zero-energy-problem'.…”