  Cohen and Glashow argued that very special conformal field theories of a
particular kind (i.e. with HOM(2) or SIM(2) invariance) cannot be constructed
within the framework of local field theories. We, however, show examples of
local construction by using non-linear realization. We further construct linear
realization from the topological twist at the cost of unitarity. To demonstrate
the ubiquity of our idea, we also present corresponding holographic models.
