8 research outputs found
The Gauged Vector Model in Four-Dimensions: Resolution of an Old Problem?
A calculation of the renormalization group improved effective potential for
the gauged U(N) vector model, coupled to fermions in the fundamental
representation, computed to leading order in 1/N, all orders in the scalar
self-coupling , and lowest order in gauge coupling , with
of order , is presented. It is shown that the theory has two phases, one of
which is asymptotically free, and the other not, where the asymptotically free
phase occurs if , and
. In the asymptotically free phase, the effective
potential behaves qualitatively like the tree-level potential. In the other
phase, the theory exhibits all the difficulties of the ungauged
vector model. Therefore the theory appears to be consistent (only) in the
asymptotically free phase.Comment: Latex, 18 pages plus 3 figures using epsf. Substantially revised to
correct a factor of 2 error in the previous version of equation (2.5b). This
has significant effects on the results. The model has also been revised to
include fermion
Quantum Kinks: Solitons at Strong Coupling
We examine solitons in theories with heavy fermions. These ``quantum''
solitons differ dramatically from semi-classical (perturbative) solitons
because fermion loop effects are important when the Yukawa coupling is strong.
We focus on kinks in a --dimensional theory coupled to
fermions; a large- expansion is employed to treat the Yukawa coupling
nonperturbatively. A local expression for the fermion vacuum energy is derived
using the WKB approximation for the Dirac eigenvalues. We find that fermion
loop corrections increase the energy of the kink and (for large ) decrease
its size. For large , the energy of the quantum kink is proportional to ,
and its size scales as , unlike the classical kink; we argue that these
features are generic to quantum solitons in theories with strong Yukawa
couplings. We also discuss the possible instability of fermions to solitons.Comment: 21 pp. + 2 figs., phyzzx, JHU-TIPAC-92001