279 research outputs found

### Non-Abelian Superconductors - Lessons from Supersymmetric Gauge Theories for QCD

Much about the confinement and dynamical symmetry breaking in QCD might be
learned from models with supersymmetry. In particular, models based on N=2
supersymmetric theories with gauge groups SU(N), SO(N) and $USp(2 N)$ and with
various number of flavors, give deep dynamical hints about these phenomena. For
instance, the BPS non-abelian monopoles can become the dominant degrees of
freedom in the infrared due to quantum effects. Upon condensation (which can be
triggered in these class of models by perturbing them with an adjoint scalar
mass) they induce confinement with calculable pattern of dynamical symmetry
breaking. This may occur either in a weakly interacting regime or in a strongly
coupled regime (in the latter, often the low-energy degrees of freedom contain
relatively non-local monopoles and dyons simultaneously and the system is near
a nontrivial fixed-point).
Also, the existence of sytems with BPS {\it non-abelian vortices} has been
shown recently. These results point toward the idea that the ground state of
QCD is a sort of dual superconductor of non-abelian variety.Comment: Latex file, 11 eps figures, Talk at the "Confinement 2003", Riken,
Tokyo, July 200

### Confinement via strongly-coupled non-Abelian monopoles

New types of confinement phase emerge as singular SCFT's appearing as
infrared-fixed-points of N=2 supersymmetric QCD (SQCD) are perturbed by an N=1
adjoint mass term. Based on a recent remarkable work on infrared-fixed-point
SCFT of highest criticalities by Gaiotto, Seiberg and Tachikawa, we discuss
physics of certain confining systems in SU(N), USp(2N) or SO(N) gauge theories.
These show features different from a straightforward dual superconductivity
picture of confinement a' la 't Hooft and Mandelstam, which might suggest a new
venue in exploring the quark confinement mechanism in the real-world QCD.Comment: Latex 17 pages. arXiv admin note: text overlap with arXiv:1301.042

### Confinement, NonAbelian monopoles, and 2D CP(N-1) model on the worldsheet of finite-length strings

Quark confinement is proposed to be a dual Meissner effect of nonAbelian
kind. Important hints come from physics of strongly-coupled
infrared-fixed-point theories in N=2 supersymmetric QCD, which turn into
confining vacua under a small relevant perturbation. The quest for the
semiclassical origin of the nonAbelian monopoles, ubiquitous as the infrared
degrees of freedom in supersymmetric gauge theories, motivates us to study the
quantum dynamics of 2D CP(N-1)model defined on a finite-width worldstrip, with
various boundary conditions. The model is found to possess a unique phase
("confinement phase"), independent of the length of the string, showing the
quantum persistence of the nonAbelian monopole.Comment: Latex 14 pages 4 figure

### Confinement, Chiral Symmetry Breaking and Faddeev-Niemi Decomposition in QCD

We identify two distinct, complementary gauge field configurations for QCD
with SU(2) gauge group, one (instanton-like configurations) having to do with
chiral symmetry breaking but not with confinement, the other (regularized
Wu-Yang monopoles) very likely responsible for confinement but unrelated to
chiral symmetry breaking. Our argument is based on a semiclassical analysis of
fermion zero modes in these backgrounds, made by use of a gauge field
decomposition recently introduced by Faddeev and Niemi. Our result suggests
that the two principal dynamical phenomena in QCD, confinement and chiral
symmetry breaking, are distinct effects, caused by two competing classes of
gauge field configurations.Comment: 13 pages, Late

### Monopole-vortex complex at large distances and nonAbelian duality

We discuss the large-distance approximation of the monopole-vortex complex
soliton in a hierarchically broken gauge system, SU(N+1) - > SU(N) x U(1) - >
1, in a color-flavor locked SU(N) symmetric vacuum. The ('t Hooft-Polyakov)
monopole of the higher-mass-scale breaking appears as a point and acts as a
source of the thin vortex generated by the lower-energy gauge symmetry
breaking. The exact color-flavor diagonal symmetry of the bulk system is broken
by each individual soliton, leading to nonAbelian orientational CP^{N-1}
zeromodes propagating in the vortex worldsheet, well studied in the literature.
But since the vortex ends at the monopoles these fluctuating modes endow the
monopoles with a local SU(N) charge. This phenomenon is studied by performing
the duality transformation in the presence of the CP^{N-1} moduli space. The
effective action is a CP^{N-1} model defined on a finite-width worldstrip.Comment: 36 pages, 4 figure

### Fermions in Instanton Anti-Instanton Background

We consider the behaviour of fermions in the background of
instanton-anti\-instanton type configurations. Several different physics
problems, from the high energy electroweak interactions to the study of vacuum
structure of QCD and of large orders of perturbation theory are related to this
problem. The spectrum of the Dirac operator in such a background is studied in
detail. We present an approximation for the fermion correlation function when
the instanton-anti\-instanton separation ($R$) is large compared to their sizes
($\rho$). The situation when the instanton-anti\-instanton overlap and melt,
is studied through the behaviour of the Chern Simons number as a function of $R/\rho$ and $x_4$.
Applying our results to widely discussed cases of fermion-number violation in
the electroweak theory, we conclude that there are no theoretical basis for
expecting anomalous cross sections to become observable at energies in $10$ TeV
region.Comment: 36 PAGES, GEF-Th-8/199

### Convergence of Scaled Delta Expansion: Anharmonic Oscillator

We prove that the linear delta expansion for energy eigenvalues of the
quantum mechanical anharmonic oscillator converges to the exact answer if the
order dependent trial frequency $\Omega$ is chosen to scale with the order as
$\Omega=CN^\gamma$; $1/30$ as $N\rightarrow\infty$. It
converges also for $\gamma=1/3$, if $C\geq\alpha_c g^{1/3}$, $\alpha_c\simeq
0.570875$, where $g$ is the coupling constant in front of the operator $q^4/4$.
The extreme case with $\gamma=1/3$, $C=\alpha_cg^{1/3}$ corresponds to the
choice discussed earlier by Seznec and Zinn-Justin and, more recently, by
Duncan and Jones.Comment: 37 pages (with 11 figures uuencoded at the end of the file,to be
stripped off), GEF-Th-7/199

### Quark Number Fractionalization in N=2 Supersymmetric $SU(2) \times U(1)^{N_f}$ Gauge Theories

Physical quark-number charges of dyons are determined, via a formula which
generalizes that of Witten for the electric charge, in N=2 supersymmetric
theories with $SU(2) \times U(1)^{N_f}$ gauge group. The quark numbers of the
massless monopole at a nondegenerate singularity of QMS turn out to vanish in
all cases. A puzzle related to CP invariant cases is solved. Generalization of
our results to $SU(N_c)\times U(1)^{N_f}$ gauge theories is straightforward.Comment: Latex file, 14 pages, 1 Postscript figur

- …