What is the Symmetry Class of Bulk Holography?

The TTbar deformation is a holographic theory describing holography a finite distance in the bulk.   If this theory can be UV completed, it could be a model of nonperturbative bulk quantum gravity.  However, it seems to be a non-unitary theory, as the energy eigenvalues lie either on the real axis or the imaginary axis.  I will describe the possible symmetry classes of (possibly non-Hermitian) Hamiltonians, and discuss which classes might be compatible with the spectrum of the TTbar deformation.