(Reverse) Engineering Vacuum Alignment

Abstract

In the presence of spontaneous symmetry breaking, the alignment of the vacuum with respect to the gauge group is often controlled by quadratically divergent operators in the low energy non-linear sigma model. In principle the magnitudes and signs of these operators can be changed by making different assumptions about the ultraviolet physics, but in practice all known ways of regulating these theories preserve the naive vacuum alignment. We show that by "integrating in" different sets of heavy spin-one fields, it is possible to UV extend certain non-linear sigma models into two distinct UV insensitive theories. These UV extensions have identical low energy degrees of freedom but different radiative potentials, making it possible to engineer two different vacuum alignments for the original non-linear sigma model. Our construction employs "non-square" theory spaces which generically violate the common lore that the preferred vacuum alignment preserves the maximal gauge symmetry. By UV extending the SO(9)/(SO(4) X SO(5)) little Higgs model, we find a radiative potential that deviates from the naive expectation but does not stabilize the correct vacuum for proper electroweak symmetry breaking.

21 pages, 6 figures, 2 tables; v2: added references, included spurion analysis

References in corpus (23)

• The Minimal Composite Higgs Model
• Electroweak symmetry breaking from dimensional deconstruction
• The Littlest Higgs
• (De)Constructing Dimensions
• The Twin Higgs: Natural Electroweak Breaking from Mirror Symmetry
• The Minimal Moose for a Little Higgs
• Higgs as a Holographic Pseudo-Goldstone Boson
• TeV Symmetry and the Little Hierarchy Problem
• Little Hierarchy, Little Higgses, and a Little Symmetry
• Little Higgses from an Antisymmetric Condensate
• T Parity and the Littlest Higgs
• The Little Higgs from a Simple Group
• A Twin Higgs Model from Left-Right Symmetry
• Weakly coupled Higgsless theories and precision electroweak tests
• A "Littlest Higgs" Model with Custodial SU(2) Symmetry
• A Simple Model of two Little Higgses
• The Intermediate Higgs
• The role of spurions in Higgs-less electroweak effective theories
• Implications for New Physics from Fine-Tuning Arguments: II. Little Higgs Models
• Little Technicolor
• Higher Derivative Operators from Transmission of Supersymmetry Breaking on S_1/Z_2
• Generalized Weinberg Sum Rules in Deconstructed QCD
• pi+ pi0 Mass Difference in the Hidden Local Symmetry: A Dynamical Origin of Little Higgs

Cited by in corpus (5)

• A Composite Twin Higgs Model
• Exotic Top Partners and Little Higgs
• Symmetry Breaking Patterns for the Little Higgs from Strong Dynamics
• Scalar Loops in Little Higgs Models
• Conformal little Higgs models