Gauge theories on an interval:  Unitarity without a Higgs boson

Abstract

We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC's) from the action principle. These BC's include choices that give rise to breaking of the gauge symmetries. The boundary conditions could be chosen to coincide with those commonly applied in orbifold theories, but there are many more possibilities. To investigate the nature of gauge symmetry breaking via BC's we calculate the elastic scattering amplitudes for longitudinal gauge bosons. We find that using a consistent set of BC's the terms in these amplitudes that explicitly grow with energy always cancel without having to introduce any additional scalar degree of freedom, but rather by the exchange of Kaluza-Klein (KK) gauge bosons. This suggests that perhaps the SM Higgs could be completely eliminated in favor of some KK towers of gauge fields. We show that from the low-energy effective theory perspective this seems to be indeed possible. We display an extra dimensional toy model, where BC's introduce a symmetry breaking pattern and mass spectrum that resembles that in the standard model.

Chiral Compactification on a Square

“…(3.18) for Ψ + L . Similar conclusions (with θ L,R replaced byθ L,R ) apply at (L, y) and (y, L): 20) and the boundary conditions are those encountered in the scalar case.…”

“…The four-dimensional scalar fields Φ (j,k) satisfy 20) where M 2 j,k is a positive eigenvalue. The f (j,k) functions are solutions to the two-dimensional equation,…”

“…In the case of five-dimensional theories, any orbifold compactification is equivalent to a set of chiral boundary conditions (see, e.g., [19]), while the reverse is not true [20,21].…”

Mesons in gauge/gravity duals

“…It is worth remarking that very similar ideas to these models have inspired the field of Higgsless electroweak models [256,257] and their deconstructed [258,259] partners for example in [260].…”

Renormalizable extra-dimensional models

“…The new approaches to solving these issues include theories with so-called universal extra dimensions which e.g. result in calculable SUSY breaking and Higgs masses [4], gauge-Higgs unification in which the Higgs field is a component of a higher dimensional gauge field whose mass is thus protected by gauge invariance [5][6][7][8][9][10][11][12][13], Higgsless models where the symmetry is broken by the boundary conditions [14], grand unified models in which colour triplet Higgs are given a Kaluza-Klein mass whilst the doublet remains massless at the compactification scale [15] (see also [16]), and approaches to the flavour problem using the freedom to place fermions at different points (branes) in the extra dimensions and to couple them non-locally through other fields or Wilson lines [9,13,[17][18][19][20].…”