1,140 research outputs found
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
Vortex counting from field theory
The vortex partition function in 2d N = (2,2) U(N) gauge theory is derived
from the field theoretical point of view by using the moduli matrix approach.
The character for the tangent space at each moduli space fixed point is written
in terms of the moduli matrix, and then the vortex partition function is
obtained by applying the localization formula. We find that dealing with the
fermionic zero modes is crucial to obtain the vortex partition function with
the anti-fundamental and adjoint matters in addition to the fundamental chiral
multiplets. The orbifold vortex partition function is also investigated from
the field theoretical point of view.Comment: 21 pages, no figure
Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d=2+1)
supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic
gauge group. In CS theory, we find topological, non-topological and semi-local
(non-)topological vortices of non-Abelian kinds in unbroken, broken and
partially broken vacua. We calculate the number of zero-modes using an index
theorem and then we apply the moduli matrix formalism to realize the moduli
parameters. For the topological solitons we exhaust all the moduli while we
study several examples of the non-topological and semi-local solitons. We find
that the zero-modes of the topological solitons are governed by the moduli
matrix H_0 only and those of the non-topological solitons are governed by both
H_0 and the gauge invariant field \Omega. We prove local uniqueness of the
master equation in the YM case and finally, compare all results between the CS
and YM theories.Comment: 54 pages, 1 figur
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
Domain walls with non-Abelian orientational moduli
Domain walls with non-Abelian orientational moduli are constructed in U(N)
gauge theories coupled to Higgs scalar fields with degenerate masses. The
associated global symmetry is broken by the domain walls, resulting in the
Nambu-Goldstone (and quasi-Nambu-Goldstone) bosons, which form the non-Abelian
orientational moduli. As walls separate, the wave functions of the non-Abelian
orientational moduli spread between domain walls. By taking the limit of Higgs
mass differences to vanish, we clarify the convertion of wall position moduli
into the non-Abelian orientational moduli. The moduli space metric and its
Kahler potential of the effective field theory on the domain walls are
constructed. We consider two models: a U(1) gauge theory with several charged
Higgs fields, and a U(N) gauge theory with 2N Higgs fields in the fundamental
representation. More details are found in our paper published in Phys. Rev. D77
(2008) 125008 [arXiv:0802.3135 [hep-th]].Comment: contribution to the Proceedings of he 1st MCCQG conference at Crete,
sept. 2009, to appear in Journal of Physics: Conference Series of IO
Radius Stabilization in a Supersymmetric Warped Compactification
A supersymmetric (SUSY) model of radius stabilization is constructed for the
S^1/Z_2 warped compactifications with a hypermultiplet in five dimensions.
Requiring the continuity of scalar field across the boundaries, we obtain
radius stabilization preserving SUSY, realizing the SUSY extension of the
Goldberger-Wise mechanism. Even if we allow discontinuities of the Z_2 odd
field across the boundary, we always obtain SUSY preservation but obtain the
radius stabilization only when the discontinuity is fixed by other mechanism.Comment: 6 pages, revtex, Errors of the products of distributions are
corrected and the results are reanalyzed, references added, final version to
appear in PR
Solitons in Supersymmety Breaking Meta-Stable Vacua
In recently found supersymmetry-breaking meta-stable vacua of the
supersymmetric QCD, we examine possible exsitence of solitons. Homotopy groups
of the moduli space of the meta-stable vacua show that there is no nontrivial
soliton for SU(N_c) gauge group. When U(1)_B symmetry present in the theory is
gauged, we find non-BPS solitonic (vortex) strings whose existence and
properties are predicted from brane configurations. We obtain explicit
classical solutions which reproduce the predicitions. For SO(N_c) gauge group,
we find there are solitonic strings for N = N_f-N_c+4 = 2, and Z_2 strings for
the other N. The strings are meta-stable as they live in the meta-stable vacua.Comment: 30 pages, 14 figures, Comments on stability of non-BPS vortices are
added, Comments on sigma model solitons are added, An appendix is adde
Vortices on Orbifolds
The Abelian and non-Abelian vortices on orbifolds are investigated based on
the moduli matrix approach, which is a powerful method to deal with the BPS
equation. The moduli space and the vortex collision are discussed through the
moduli matrix as well as the regular space. It is also shown that a quiver
structure is found in the Kahler quotient, and a half of ADHM is obtained for
the vortex theory on the orbifolds as the case before orbifolding.Comment: 25 pages, 4 figures; references adde
Exploratory analysis of high-resolution power interruption data reveals spatial and temporal heterogeneity in electric grid reliability
Modern grid monitoring equipment enables utilities to collect detailed
records of power interruptions. These data are aggregated to compute publicly
reported metrics describing high-level characteristics of grid performance. The
current work explores the depth of insights that can be gained from public
data, and the implications of losing visibility into heterogeneity in grid
performance through aggregation. We present an exploratory analysis examining
three years of high-resolution power interruption data collected by archiving
information posted in real-time on the public-facing website of a utility in
the Western United States. We report on the size, frequency and duration of
individual power interruptions, and on spatio-temporal variability in aggregate
reliability metrics. Our results show that metrics of grid performance can vary
spatially and temporally by orders of magnitude, revealing heterogeneity that
is not evidenced in publicly reported metrics. We show that limited access to
granular information presents a substantive barrier to conducting detailed
policy analysis, and discuss how more widespread data access could help to
answer questions that remain unanswered in the literature to date. Given open
questions about whether grid performance is adequate to support societal needs,
we recommend establishing pathways to make high-resolution power interruption
data available to support policy research.Comment: Journal submission (in review), 22 pages, 8 figures, 1 tabl
Static Interactions of non-Abelian Vortices
Interactions between non-BPS non-Abelian vortices are studied in non-Abelian
U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The
distinctive feature of a non-Abelian vortex is the presence of an internal
CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of
the couplings, the vortices are BPS and there is no net force between two
static parallel vortices at arbitrary distance. On the other hand, for generic
values of the couplings the interactions between two vortices depend
non-trivially on their relative internal orientations. We discuss the problem
both with a numerical approach (valid for small deviations from the BPS limit)
and in a semi-analytical way (valid at large vortex separations). The
interactions can be classified with respect to their asymptotic property at
large vortex separation. In a simpler fine-tuned model, we find two regimes
which are quite similar to the usual type I/II Abelian superconductors. In the
generic model we find other two new regimes: type I*/II*. Unlike the type I
(type II) case, where the interaction is always attractive (repulsive), the
type I* and II* have both attractive and repulsive interactions depending on
the relative orientation. We have found a rich variety of interactions at small
vortex separations. For some values of the couplings, a bound state of two
static vortices at a non-zero distance exists.Comment: 36 pages, 13 figures; v2 a small comment and a reference adde
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