Joint analysis of the energy spectrum of ultra-high-energy cosmic rays measured at the Pierre Auger Observatory and the Telescope Array Yoshiki Tsunesada , * on behalf of the Pierre Auger and the Telescope Array Collaboration

The technique for constructing conformally invariant theories within the coset space construction is developed. It reproduces all consequences of the conformal invariance and Lagrangians of widely known conformal field theories. The method of induced representations, which plays the key role in the construction, allows us to reveal a special role of the Nambu-Goldstone fields for special conformal transformations. Namely, their dependence on the coordinates turns out to be fixed by the symmetries. This results in the appearance of the constraints on possible forms of Lagrangians, which ensure that discrete symmetries are indeed symmetries of the theory.

We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the infrared. Holographic description of the strong coupling is used. The emphasis is made on emergence of chiral fermions in the low-energy theory.