Temporary Grand Unified Theory in Unphysical World

Recently, a grand unification scenario in unphysical world has been proposed.1) The basic idea is as follows. Fields form multiplets under a unified gauge group and the gauge coupling unification originates from the gauge symmetry at a high-energy scale, as ordinary grand unified theories (GUTs).2), 3) Some members in multiples, however, are unphysical degrees of freedom, which are eliminated by a large local symmetry, under specific field configurations. Then no full unified symmetry is realized in the physical world. If physical fields are the multiples of the standard model (SM) gauge group and survive in the low-energy scale, we can understand why the SM particles (and their superpartners) play an essential role in our world and the stability of proton.∗∗) We refer to our scenario as topological grand unification or unphysical grand unification. In our scenario, the question at hand is how to formulate a grand unified theory including unphysical modes. We assume that a Lagrangian density LU , which possesses a large local symmetry and a unified gauge symmetry, is dynamically and temporarily derived from a more fundamental theory. Our goal is that we arrive at the SM or a supersymmetric SM (SSM) after the reduction of unphysical modes. Specifically, after eliminating extra degrees of freedom including extra coordinates, we would like to obtain the action integral of the SM or SSM