Abstract
We study the vacua of an $SU(3)\times SU(3)$-symmetric model with a bifundamental scalar. Structures of this type appear in various gauge theories such as the Renormalizable Coloron Model, which is an extension of QCD, or the Trinification extension of the electroweak group. In other contexts, such as chiral symmetry, $SU(3)\times SU(3)$ is a global symmetry. As opposed to more general $SU(N)\times SU(N)$ symmetric models, the $N=3$ case is special due to the presence of a trilinear scalar term in the potential. We find that the most general tree-level potential has only three types of minima: one that preserves the diagonal $SU(3)$ subgroup, one that is $SU(2)\times SU(2)\times U(1)$ symmetric, and a trivial one where the full symmetry remains unbroken. The phase diagram is complicated, with some regions where there is a unique minimum, and other regions where two minima coexist.
Highlights
Several quantum field theories of interest for physics beyond the Standard Model have an SUð3Þ × SUð3Þ symmetry, which is spontaneously broken
The embedding of the QCD gauge group, SUð3Þc, into an SUð3Þ1 × SUð3Þ2 gauge symmetry has been considered in various contexts, including dynamical symmetry breaking [1], rare Z decays [2], the study of heavy color-octet spin-1 particles such as the axigluon [3,4] or the coloron [5,6], composite Higgs models based on the top-seesaw mechanism [7], and so on
A simple structure that achieves that breaking consists of a single scalar field that transforms in the bifundamental representation, with a potential that includes a trilinear interaction, as discussed in the renormalizable coloron model (ReCoM) [8,9,10]
Summary
Several quantum field theories of interest for physics beyond the Standard Model have an SUð3Þ × SUð3Þ symmetry, which is spontaneously broken. The embedding of the QCD gauge group, SUð3Þc, into an SUð3Þ1 × SUð3Þ2 gauge symmetry has been considered in various contexts, including dynamical symmetry breaking [1], rare Z decays [2], the study of heavy color-octet spin-1 particles such as the axigluon [3,4] or the coloron [5,6], composite Higgs models based on the top-seesaw mechanism [7], and so on. We will prove that such patterns of symmetry breaking are not possible, even when the vacuum resides in a local minimum instead of a global minimum Another question (partially addressed in [9,18]) is about the asymptotic behavior of the potential: what ranges of parameters make the potential bounded from below? There is a minimum with VðΣÞ 1⁄4 0 at s1 1⁄4 s2 1⁄4 s3 1⁄4 0 provided m2Σ < 0
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