Conformality, Particle Phenomenology and the Cosmological Constant

Abstract

Conformality is the idea that at TeV scales enrichment of the standard model particle spectrum leads to conformal invariance at a fixed point of the renormalization group. Some aspects of conformality in particle phenomenology and cosmology are discussed. Alternative to "Grand" UnificationIn GUT theories there is an unexplained hierarchy between the GUT scale and the weak scale which is about 14 orders of magnitude. There is the question of why these very different scales exist and how are the scales stabilized under quantum corrections? Supersymmetry solves the second of these problems but not the first. Supersymmetry has some successes: (i) the cancellation of some UV divergences; (ii) the technical naturalness of the hierarchy; (iii) the unification of the gauge couplings; and (iv) its natural appearance in string theory.On the other side, supersymmetry definitely presents several puzzles: (i) the "mu" problem -why is the Higgs at the weak scale not at the GUT scale?; (ii) breaking supersymmetry leads to too large a cosmological constant; and (iii) is supersymmetry really fundamental for string theory since there are solutions of string theory without supersymmetry.These general considerations led naturally to the suggestion [1,2,3,4,5,6] that supersymmetry and grand unification should be replaced by conformality at the TeV scale. Here it will be shown that this idea is possible, including explicit examples containing the standard model states. Further it will be shown that conformality is a much more rigid constraint than supersymmetry. Conformality predicts additional states at the TeV scale and a rich inter-family structure of Yukawa couplings.