90 research outputs found
Non-Abelian Walls in Supersymmetric Gauge Theories
The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed
in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C)
hypermultiplets in the fundamental representation. Exact solutions are obtained
with full generic moduli for infinite gauge coupling and with partial moduli
for finite gauge coupling. The generic wall solutions require nontrivial
configurations for either gauge fields or off-diagonal components of adjoint
scalars depending on the gauge. Effective theories of moduli fields are
constructed as world-volume gauge theories. Nambu-Goldstone and
quasi-Nambu-Goldstone scalars are distinguished and worked out. Total moduli
space of the BPS non-Abelian walls including all topological sectors is found
to be the complex Grassmann manifold SU(N_F) / [SU(N_C) x SU(N_F-N_C) x U(1)]
endowed with a deformed metric.Comment: 62 pages, 17 figures, the final version in PR
Non-Abelian vortex dynamics: Effective world-sheet action
The low-energy vortex effective action is constructed in a wide class of
systems in a color-flavor locked vacuum, which generalizes the results found
earlier in the context of U(N) models. It describes the weak fluctuations of
the non-Abelian orientational moduli on the vortex worldsheet. For instance,
for the minimum vortex in SO(2N) x U(1) or USp(2N) x U(1) gauge theories, the
effective action found is a two-dimensional sigma model living on the Hermitian
symmetric spaces SO(2N)/U(N) or USp(2N)/U(N), respectively. The fluctuating
moduli have the structure of that of a quantum particle state in spinor
representations of the GNO dual of the color-flavor SO(2N) or USp(2N) symmetry,
i.e. of SO(2N) or of SO(2N+1). Applied to the benchmark U(N) model our
procedure reproduces the known CP(N-1) worldsheet action; our recipe allows us
to obtain also the effective vortex action for some higher-winding vortices in
U(N) and SO(2N) theories.Comment: LaTeX, 25 pages, 0 figure
Stable vs Unstable Vortices in SQCD
We give a topological classification of stable and unconfined massive
particles and strings (and some instantons) in worldvolume theories of
M5-branes and their dimensional reductions, generalizing Witten's
classification of strings in SYM. In particular 4d N=2 SQCD softly broken to
N=1 contains torsion (Douglas-Shenker) Z_N-strings and nontorsion (Hanany-Tong)
Z-strings. Some of the former are stable when the flavor symmetry is gauged,
while those that are not stable confine quarks and in some vacua even dyons
into baryons. The nontorsion strings are stable if and only if all colors are
locked to flavors, which is weaker than the BPS condition. As a byproduct
unstable string decay modes and approximate lifetimes are found. Cascading
theories have no vortices stabilized by the topological charges treated here
and in particular Gubser-Herzog-Klebanov axionic strings do not carry such a
charge.Comment: 32 pages, 6 figure
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
Global Structure of Moduli Space for BPS Walls
We study the global structure of the moduli space of BPS walls in the Higgs
branch of supersymmetric theories with eight supercharges. We examine the
structure in the neighborhood of a special Lagrangian submanifold M, and find
that the dimension of the moduli space can be larger than that naively
suggested by the index theorem, contrary to previous examples of BPS solitons.
We investigate BPS wall solutions in an explicit example of M using Abelian
gauge theory. Its Higgs branch turns out to contain several special Lagrangian
submanifolds including M. We show that the total moduli space of BPS walls is
the union of these submanifolds. We also find interesting dynamics between BPS
walls as a byproduct of the analysis. Namely, mutual repulsion and attraction
between BPS walls sometimes forbid a movement of a wall and lock it in a
certain position; we also find that a pair of walls can transmute to another
pair of walls with different tension after they pass through.Comment: 42 pages, 11 figures; a few comments adde
Vortex Strings and Four-Dimensional Gauge Dynamics
We study the low-energy quantum dynamics of vortex strings in the Higgs phase
of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is
shown to coincide with the BPS spectrum of the four-dimensional parent gauge
theory. Perturbative string excitations correspond to bound W-bosons and quarks
while the monopoles appear as kinks on the vortex string. This provides a
physical explanation for an observation by N. Dorey relating the quantum
spectra of theories in two and four dimensions.Comment: 23 pages, 1 figure. v2: Two extra appendices included: one on the
brane construction, the other describing the potential on the vortex moduli
space. Two figures added. Typos corrected and references added. v3: BPS
nature of quarks correcte
Dark matter production from cosmic necklaces
Cosmic strings have gained a great interest, since they are formed in a large
class of brane inflationary models. The most interesting story is that cosmic
strings in brane models are distinguished in future cosmological observations.
If the strings in brane models are branes or superstrings that can move along
compactified space, and also if there are degenerated vacua along the
compactified space, kinks interpolate between degenerated vacua become
``beads'' on the strings. In this case, strings turn into necklaces. In the
case that the compact manifold in not simply connected, a string loop that
winds around a nontrivial circle is stable due to the topological reason. Since
the existence of the (quasi-)degenerated vacua and the nontrivial circle is a
common feature of the brane models, it is important to study cosmological
constraints on the cosmic necklaces and the stable winding states. In this
paper, we consider dark matter production from loops of the cosmic necklaces.
Our result suggests that necklaces can put stringent bound on certain kinds of
brane models.Comment: 27 pages, 5 figures, added many comments and 3 figures, accepted for
publication in JCA
Elliptic Inflation: Generating the curvature perturbation without slow-roll
There are many inflationary models in which inflaton field does not satisfy
the slow-roll condition. However, in such models, it is always difficult to
generate the curvature perturbation during inflation. Thus, to generate the
curvature perturbation, one must introduce another component to the theory. To
cite a case, curvatons may generate dominant part of the curvature perturbation
after inflation. However, we have a question whether it is unrealistic to
consider the generation of the curvature perturbation during inflation without
slow-roll. Assuming multi-field inflation, we encounter the generation of the
curvature perturbation during inflation without slow-roll. The potential along
equipotential surface is flat by definition and thus we do not have to worry
about symmetry. We also discuss about KKLT models, in which corrections lifting
the inflationary direction may not become a serious problem if there is a
symmetry enhancement at the tip (not at the moving brane) of the inflationary
throat.Comment: 27pages, 8figures, to appear in JCA
Group Theory of Non-Abelian Vortices
We investigate the structure of the moduli space of multiple BPS non-Abelian
vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our
attention on the action of the exact global (color-flavor diagonal) SU(N)
symmetry on it. The moduli space of a single non-Abelian vortex, CP(N-1), is
spanned by a vector in the fundamental representation of the global SU(N)
symmetry. The moduli space of winding-number k vortices is instead spanned by
vectors in the direct-product representation: they decompose into the sum of
irreducible representations each of which is associated with a Young tableau
made of k boxes, in a way somewhat similar to the standard group composition
rule of SU(N) multiplets. The K\"ahler potential is exactly determined in each
moduli subspace, corresponding to an irreducible SU(N) orbit of the
highest-weight configuration.Comment: LaTeX 46 pages, 4 figure
Supersymmetry Breaking on Gauged Non-Abelian Vortices
There are a large number of systems characterized by a completely broken
gauge symmetry, but with an unbroken global color-flavor diagonal symmetry,
i.e., systems in the so-called color-flavor locked phase. If the gauge symmetry
breaking supports vortices, the latter develop non-Abelian orientational
zero-modes and become non-Abelian vortices, a subject of intense study in the
last several years. In this paper we consider the effects of weakly gauging the
full exact global flavor symmetry in such systems, deriving an effective
description of the light excitations in the presence of a vortex. Surprising
consequences are shown to follow. The fluctuations of the vortex orientational
modes get diffused to bulk modes through tunneling processes. When our model is
embedded in a supersymmetric theory, the vortex is still 1/2 BPS saturated, but
the vortex effective action breaks supersymmetry spontaneously.Comment: Latex, 24 pages, 1 figur
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