FC Sets and Twisters: The Basics of Orbifold Deconstruction

We present a detailed account of the properties of $$\text {twister}$$ twister s and their generalizations, $$\text {FC set}$$ FC set s, which are essential ingredients of the orbifold deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and if so, to identify the twist group and the original model. The close analogy with the character theory of finite groups is discussed, and its origin explained.

The fine tuning of the cosmological constant in a conformal model

We consider a conformal model involving two real scalar fields in which the conformal symmetry is broken by a soft mechanism and is not anomalous. One of these scalar fields is representative of the standard model Higgs. The model predicts exactly zero cosmological constant. In the simplest version of the model, some of the couplings need to be fine-tuned to very small values. We formulate the problem of fine tuning of these couplings. We argue that the problem arises since we require a soft mechanism to break conformal symmetry. The symmetry breaking is possible only if the scalar fields do not evolve significantly over the time scale of the Universe. Ignoring contributions due to quantum gravity, we present two solutions to this fine tuning problem. We argue that the problem is solved if the classical value of one of the scalar fields is super-Planckian, i.e. takes a value much larger than the Planck mass. The second solution involves introduction of a strongly coupled hidden sector that we call hypercolor. In this case, the conformal invariance is broken dynamically and triggers the breakdown of the electroweak symmetry. We argue that our analysis applies also to the case of the standard model Higgs multiplet.