Lifshitz Phase Gauge Symmetry Breaking and Application to E 6 and E 8 Grand Unification

When a gauge theory with gauge group G is broken by a dynamical condensate C that transforms nontrivially under G, with covariant derivative (DμC) , the leading derivative term (DμC) (DC)A in the effective action can have a coefficient α of general sign and magnitude. The case α > 0 corresponds to the usual Higgs phase, but the cases α = 0 and α < 0 correspond to new phases with novel properties. We term the α = 0 case the “null” or “Lifshitz phase”, because of the analogy with the Lifshitz point of condensed matter physics. In the Lifshitz phase, the Goldstone bosons with quantum numbers corresponding to the broken gauge generators appear as physical states. We discuss scenarios that arise if various grand unification groups were to break through a Lifshitz phase, and show that in the cases of E6 and E8, the Goldstone multiplets would contain a scalar with the correct quantum numbers to be the standard model Higgs boson. We show that starting from supersymmetric E8, forces mediated by even spin bosons generate a plausible gauge breaking hierarchy leading to the standard model.