Higgs Potentials Research Articles

Extrema of Higgs potentials and higher representations

The problem of symmetry breaking is studied. A method suitable for higher-rank tensors is suggested. This method is used to break SU(2n)..-->..SU(n) x SU(n) x U(1) via the traceless symmetric fourth-rank tensor T/sup opening-bracea/b)/sub opening-bracec/d).

General method for analyzing Higgs potentials

We define a set of group-invariant orbit parameters. Using them, we describe a method for determining the energy and residual symmetry of the Higgs potential minimum. The method is general, and offers significant advantages in analyzing complicated Higgs potentials.

SU( N) Higgs problem with adjoint representation, and Michel's conjecture

Recently a geometrical method has been devised for analyzing the minimum of complicated Higgs potentials. Using the method we analyze the general quartic Higgs potential, including cubic coupling, for SU( N) adjoint representation. The task of proving Michel's conjecture is reduced to showing that the orbit space is generally “star-shaped”.

Group-theoretical determination of minima of Higgs potentials

We develop a group-theoretical method to determine the extrema of invariant Higgs potentials of degree four without cubic terms. It applies successfully to the adjoint representations of theO(8+2n) andSU(3+n) groups and to the spinorial representation ofO(14). We give also a method to compute invariants which is very useful for critical orbits.

Horizontal symmetry and pseudo-goldstone bosons

We investigate the minimization problem of Higgs potentials invariant under a semisimple gauge group of the form G V × G H. G V is taken to be the SU(2) × U(1) electroweak group and G H, a horizontal symmetry group, is either SU(2) or SU(3). The different possibilities of G H representation for the Higgs fields are considered in turn, and in most cases we find that the minimum of the corresponding potential is such that pseudo-Goldstone bosons occur.

The geometry of orbit-space and natural minima of Higgs potentials

Starting from an analysis of the geometry of orbit-space, we propose a new approach to the determination of those extrema of a G-invariant C ∞-function (G is a compact linear group), which are associated to an arbitrary, but fixed, residual symmetry group. When applied to Higgs potentials of unified gauge field theories, the method allows one to state conditions for the minima to exist and be natural (stable) and to clarify the origin of a class of pseudo-Goldstone bosons.

The geometrical significance of certain Higgs potentials: An approach to grand unification

It is pointed out that the Higgs potentials in certain Yang-Mills-Higgs theories are natural, in the sense that they can be derived by dimensionally reducing pure Yang-Mills theories defined in more than four space-time dimensions. In particular, when the symmetry group of the space of extra dimensions is a subgroup of the initial gauge group, then the Higgs potential can be given a purely group-theoretic interpretation. An interesting class of grand-unified-like models with Higgs potentials of this type can be derived using the exceptional group E 8 as initial gauge group. One property of these models is that they are characterized by very few arbitrary parameters; nevertheless, a hierarchy of gauge symmetry breaking is still possible.

Isotropy subgroups of SO(3) and Higgs potentials

A method is given for determining the isotropy subgroups of an arbitrary, irreducible representation of SO(3). These subgroups are explicitly worked out for low-dimensional representations. As an application of these results we contruct the most general, renormalizable, SO(3) invariant Higgs potentials for these representations, determine the local minima of the potentials and discuss patterns of spontaneous symmetry breaking.