Abstract
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.
Highlights
The assumption of locality plays an essential role in relativistic quantum field theories
It is usually argued that locality is necessary to guarantee the causal structure that is compatible with the special relativity: “nothing can travel faster than the speed of light.”
Cohen and Glashow argued that the locality may play a significant role in very special relativity [1,2], which is a certain subgroup of Lorentz symmetry that preserves a particular null direction
Summary
The assumption of locality plays an essential role in relativistic quantum field theories. Cohen and Glashow argued that the locality may play a significant role in very special relativity [1,2], which is a certain subgroup of Lorentz symmetry that preserves a particular null direction. They claim that if they impose the locality in field theories that obey a certain class of the very special relativity, they must be fully Lorentz invariant. Cohen and Glashow found that there are no such local operators available from the representation theory of Lorentz algebra They argue that there are no local field theories that realize SIM(2) and HOM(2) invariant very special relativity without symmetry enhancement to the full Lorentz symmetry. We show some examples in the context of very special conformal field theories [4] for definiteness, but a similar construction is possible and obviously easier without imposing the conformal symmetry
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