Are quarks and leptons dynamically confined in four flat extra dimensions?

Abstract

Rubakov and Shaposhnikov have shown that the domain wall generated by real one-component φ 4 theory extended to five flat (non-compact) dimensions can trap a massive bosonic excitation on the wall M 4; adding L D = i Σ μ=0 4 ψγ μ∂ μψ + g ψφψ likewise traps a massless left-chiral Dirac particle on the wall. Independently, Kaplan has proposed this same mechanism to generate a massless chiral fermion to circumvent no-go theorems in lattice gauge theories. We show that if the Dirac field equation is extended to (7+1) flat dimensions and the classical domain wall replaced in the four extra dimensions R 4 by a harmonic-oscillator potential plus a large constant, then “orbital” times “spin” solutions are generated in R 4 which exhibit approximate SU(4) × SU(2) symmetry. In an SU(4) = SU(3) × U(1) decomposition, the 1 and 3 irreps of SU(3) resemble singlet and triplet color, respectively, while the U(1) symmetry yields replications suggesting generation number. Doublet representations of SU(2) resemble weak isospin. Thus these representations bear some resemblance to quarks and leptons. We indicate an SU(3)-invariant coupling of gluons to these “quarks”, and a left-right symmetric coupling of the proposed quarks and “leptons” to electroweak bosons. We suggest looking for an alternate mechanism to the HO well, perhaps a (Euclidean) instanton.