Abstract
We present a class of field configurations that are forbidden in the quantum gravity because of inconsistency in the dual field theory from holography. Scale invariant but non-conformal field theories are impossible in (1+1) dimension under some mild assumptions such as unitarity, and so should be the corresponding gravity dual. In particular, the ``spontaneous Lorentz symmetry breaking" models and the ``ghost condensation" models, which are well-studied in phenomenology literatures, are forbidden in any consistent quantum theories of gravity in (1+2) dimension since they predict such inconsistent field configurations.
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