Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode a generic coordinate system. show that satisfies three-dimensional elliptic differential equation on spacelike hypersurface, hence it does not propagate. clarify how to treat this “shadowy” at both linear nonlinear levels.

The higher-order tensor renormalization group is a tensor-network method providing estimates for the partition function and thermodynamical observables of classical quantum systems in thermal equilibrium. At every step iterative blocking procedure, coarse-grid truncated to keep dimension under control. For consistent it crucial that forward backward modes are projected on same lower dimensional...