Local field theory construction of Very Special Conformal Symmetry

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 sacrifice of unitarity. To demonstrate the ubiquity of our idea, we also present corresponding holographic models.