6 research outputs found
Confinement and Localization on Domain Walls
We continue the studies of localization of the U(1) gauge fields on domain
walls. Depending on dynamics of the bulk theory the gauge field localized on
the domain wall can be either in the Coulomb phase or squeezed into flux tubes
implying (Abelian) confinement of probe charges on the wall along the wall
surface. First, we consider a simple toy model with one flavor in the bulk at
weak coupling (a minimal model) realizing the latter scenario. We then suggest
a model presenting an extension of the Seiberg--Witten theory which is at
strong coupling, but all theoretical constructions are under full control if we
base our analysis on a dual effective action. Finally, we compare our findings
with the wall in a "nonminimal" theory with two distinct quark flavors that had
been studied previously. In this case the U(1) gauge field trapped on the wall
is exactly massless because it is the Goldstone boson of a U(1) symmetry in the
bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb
phase. We explain why the mechanism of confinement discussed in the first part
of the paper does not work in this case, and strings are not formed on the
walls.Comment: 55 pp; v2: several remarks adde
Strings Inside Walls in N=1 Super Yang-Mills
We conjecture the existence of strings bounded inside walls in SU
Super Yang-Mills theory. These strings carry quantum number, where
is the greatest common divisor between , the charge of the wall, and
. We provide field-theoretical arguments and string-theoretical evidences,
both from MQCD and from gauge-gravity correspondence. We interpret this result
from the point of view of the low-energy effective action living on the
-wall.Comment: 25 pp. Major changes. In particular, following the recent work
arXiv:0807.1908 we have been able to give a field theoretical proof of the
statement. We have also corrected an important erroneous interpretation in
the previous version regarding the 2+1 effective action; Typo
Solitons in the Higgs phase -- the moduli matrix approach --
We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge
theory with N_F Higgs scalar fields in the fundamental representation, which
can be extended to possess eight supercharges. We propose the moduli matrix as
a fundamental tool to exhaust all BPS solutions, and to characterize all
possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices,
which are the only elementary solitons in the Higgs phase, are found in terms
of the moduli matrix. Stable monopoles and instantons can exist in the Higgs
phase if they are attached by vortices to form composite solitons. The moduli
spaces of these composite solitons are also worked out in terms of the moduli
matrix. Webs of walls can also be formed with characteristic difference between
Abelian and non-Abelian gauge theories. We characterize the total moduli space
of these elementary as well as composite solitons. Effective Lagrangians are
constructed on walls and vortices in a compact form. We also present several
new results on interactions of various solitons, such as monopoles, vortices,
and walls. Review parts contain our works on domain walls (hep-th/0404198,
hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices
(hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135,
hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129,
hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective
Lagrangian on walls and vortices (hep-th/0602289), classification of BPS
equations (hep-th/0506257), and Skyrmions (hep-th/0508130).Comment: 89 pages, 33 figures, invited review article to Journal of Physics A:
Mathematical and General, v3: typos corrected, references added, the
published versio