Possible Non-Higgs Symmetry Breaking Phases in Gauge Theories

When a theory with gauged symmetry G is broken to a theory with smaller gauged symmetry H by a dynamical condensate C, transforming as a singlet underH but 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 respectively to new “null” and “tachyonic” phases with potentially novel properties. We analyze the “null” case in detail, and show that the Goldstone bosons in this phase, rather than being swallowed by the Higgs mechanism, are confined into Goldstone composites by the unbroken H gauge force. Residual gauge transformations of G, when correlated as H singlets, produce non-Abelian mixings of these composites under an induced gauge group K. When the condensate C is a K singlet, gauge invariance of the effective action then implies that there must also be induced composite gauge bosons in the adjoint of K, which appear in covariant derivatives of the Goldstone composites in the effective action. We illustrate the group theory with an explicit calculation for the case G = SU(n + 1), H = SU(n) × U(1), for which the Goldstone composites form a triplet (together with an additional singlet) under an induced SU(2) gauge group. Possible relevance of this mechanism to electroweak dynamical symmetry breaking is briefly discussed.