2,045 research outputs found

### On The Phase Transition in D=3 Yang-Mills Chern-Simons Gauge Theory

$SU(N)$ Yang-Mills theory in three dimensions, with a Chern-Simons term of
level $k$ (an integer) added, has two dimensionful coupling constants, $g^2 k$
and $g^2 N$; its possible phases depend on the size of $k$ relative to $N$. For
$k \gg N$, this theory approaches topological Chern-Simons theory with no
Yang-Mills term, and expectation values of multiple Wilson loops yield Jones
polynomials, as Witten has shown; it can be treated semiclassically. For $k=0$,
the theory is badly infrared singular in perturbation theory, a
non-perturbative mass and subsequent quantum solitons are generated, and Wilson
loops show an area law. We argue that there is a phase transition between these
two behaviors at a critical value of $k$, called $k_c$, with $k_c/N \approx 2
\pm .7$. Three lines of evidence are given: First, a gauge-invariant one-loop
calculation shows that the perturbative theory has tachyonic problems if $k
\leq 29N/12$.The theory becomes sensible only if there is an additional dynamic
source of gauge-boson mass, just as in the $k=0$ case. Second, we study in a
rough approximation the free energy and show that for $k \leq k_c$ there is a
non-trivial vacuum condensate driven by soliton entropy and driving a
gauge-boson dynamical mass $M$, while both the condensate and $M$ vanish for $k
\geq k_c$. Third, we study possible quantum solitons stemming from an effective
action having both a Chern-Simons mass $m$ and a (gauge-invariant) dynamical
mass $M$. We show that if M \gsim 0.5 m, there are finite-action quantum
sphalerons, while none survive in the classical limit $M=0$, as shown earlier
by D'Hoker and Vinet. There are also quantum topological vortices smoothly
vanishing as $M \rightarrow 0$.Comment: 36 pages, latex, two .eps and three .ps figures in a gzipped
uuencoded fil

### On One-Loop Gap Equations for the Magnetic Mass in d=3 Gauge Theory

Recently several workers have attempted determinations of the so-called
magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap
equation, using a free massive propagator as input. Self-consistency is
attained only on-shell, because the usual Feynman-graph construction is
gauge-dependent off-shell. We examine two previous studies of the pinch
technique proper self-energy, which is gauge-invariant at all momenta, using a
free propagator as input, and show that it leads to inconsistent and unphysical
result. In one case the residue of the pole has the wrong sign (necessarily
implying the presence of a tachyonic pole); in the second case the residue is
positive, but two orders of magnitude larger than the input residue, which
shows that the residue is on the verge of becoming ghostlike. This happens
because of the infrared instability of d=3 gauge theory. A possible alternative
one-loop determination via the effective action also fails. The lesson is that
gap equations must be considered at least at two-loop level.Comment: 21 pages, LaTex, 2 .eps figure

### Center vortices and confinement vs. screening

We study adjoint and fundamental Wilson loops in the center-vortex picture of
confinement, for gauge group SU(N) with general N. There are N-1 distinct
vortices, whose properties, including collective coordinates and actions, we
study. In d=2 we construct a center-vortex model by hand so that it has a
smooth large-N limit of fundamental-representation Wilson loops and find, as
expected, confinement. Extending an earlier work by the author, we construct
the adjoint Wilson-loop potential in this d=2 model for all N, as an expansion
in powers of $\rho/M^2$, where $\rho$ is the vortex density per unit area and M
is the vortex inverse size, and find, as expected, screening. The leading term
of the adjoint potential shows a roughly linear regime followed by string
breaking when the potential energy is about 2M. This leading potential is a
universal (N-independent at fixed fundamental string tension $K_F$) of the form
$(K_F/M)U(MR)$, where R is the spacelike dimension of a rectangular Wilson
loop. The linear-regime slope is not necessarily related to $K_F$ by Casimir
scaling. We show that in d=2 the dilute vortex model is essentially equivalent
to true d=2 QCD, but that this is not so for adjoint representations; arguments
to the contrary are based on illegal cumulant expansions which fail to
represent the necessary periodicity of the Wilson loop in the vortex flux. Most
of our arguments are expected to hold in d=3,4 also.Comment: 29 pages, LaTex, 1 figure. Minor changes; references added;
discussion of factorization sharpened. Major conclusions unchange

### Center Vortices, Nexuses, and the Georgi-Glashow Model

In a gauge theory with no Higgs fields the mechanism for confinement is by
center vortices, but in theories with adjoint Higgs fields and generic symmetry
breaking, such as the Georgi-Glashow model, Polyakov showed that in d=3
confinement arises via a condensate of 't Hooft-Polyakov monopoles. We study
the connection in d=3 between pure-gauge theory and the theory with adjoint
Higgs by varying the Higgs VEV v. As one lowers v from the Polyakov semi-
classical regime v>>g (g is the gauge coupling) toward zero, where the unbroken
theory lies, one encounters effects associated with the unbroken theory at a
finite value v\sim g, where dynamical mass generation of a gauge-symmetric
gauge- boson mass m\sim g^2 takes place, in addition to the Higgs-generated
non-symmetric mass M\sim vg. This dynamical mass generation is forced by the
infrared instability (in both 3 and 4 dimensions) of the pure-gauge theory. We
construct solitonic configurations of the theory with both m,M non-zero which
are generically closed loops consisting of nexuses (a class of soliton recently
studied for the pure-gauge theory), each paired with an antinexus, sitting like
beads on a string of center vortices with vortex fields always pointing into
(out of) a nexus (antinexus); the vortex magnetic fields extend a transverse
distance 1/m. An isolated nexus with vortices is continuously deformable from
the 't Hooft-Polyakov (m=0) monopole to the pure-gauge nexus-vortex complex
(M=0). In the pure-gauge M=0 limit the homotopy $\Pi_2(SU(2)/U(1))=Z_2$ (or its
analog for SU(N)) of the 't Hooft monopoles is no longer applicable, and is
replaced by the center-vortex homotopy $\Pi_1(SU)N)/Z_N)=Z_N$.Comment: 27 pages, LaTeX, 3 .eps figure

### Center Vortices, Nexuses, and Fractional Topological Charge

It has been remarked in several previous works that the combination of center
vortices and nexuses (a nexus is a monopole-like soliton whose world line
mediates certain allowed changes of field strengths on vortex surfaces) carry
topological charge quantized in units of 1/N for gauge group SU(N). These
fractional charges arise from the interpretation of the standard topological
charge integral as a sum of (integral) intersection numbers weighted by certain
(fractional) traces. We show that without nexuses the sum of intersection
numbers gives vanishing topological charge (since vortex surfaces are closed
and compact). With nexuses living as world lines on vortices, the contributions
to the total intersection number are weighted by different trace factors, and
yield a picture of the total topological charge as a linking of a closed nexus
world line with a vortex surface; this linking gives rise to a non-vanishing
but integral topological charge. This reflects the standard 2\pi periodicity of
the theta angle. We argue that the Witten-Veneziano relation, naively violating
2\pi periodicity, scales properly with N at large N without requiring 2\pi N
periodicity. This reflects the underlying composition of localized fractional
topological charge, which are in general widely separated. Some simple models
are given of this behavior. Nexuses lead to non-standard vortex surfaces for
all SU(N) and to surfaces which are not manifolds for N>2. We generalize
previously-introduced nexuses to all SU(N) in terms of a set of fundamental
nexuses, which can be distorted into a configuration resembling the 't
Hooft-Polyakov monopole with no strings. The existence of localized but
widely-separated fractional topological charges, adding to integers only on
long distance scales, has implications for chiral symmetry breakdown.Comment: 15 pages, revtex, 6 .eps figure

### Nexus solitons in the center vortex picture of QCD

It is very plausible that confinement in QCD comes from linking of Wilson
loops to finite-thickness vortices with magnetic fluxes corresponding to the
center of the gauge group. The vortices are solitons of a gauge-invariant QCD
action representing the generation of gluon mass. There are a number of other
solitonic states of this action. We discuss here what we call nexus solitons,
in which for gauge group SU(N), up to N vortices meet a a center, or nexus,
provided that the total flux of the vortices adds to zero (mod N). There are
fundamentally two kinds of nexuses: Quasi-Abelian, which can be described as
composites of Abelian imbedded monopoles, whose Dirac strings are cancelled by
the flux condition; and fully non-Abelian, resembling a deformed sphaleron.
Analytic solutions are available for the quasi-Abelian case, and we discuss
variational estimates of the action of the fully non-Abelian nexus solitons in
SU(2). The non-Abelian nexuses carry Chern-Simons number (or topological charge
in four dimensions). Their presence does not change the fundamentals of
confinement in the center-vortex picture, but they may lead to a modified
picture of the QCD vacuum.Comment: LateX, 24 pages, 2 .eps figure

### On the connection between the pinch technique and the background field method

The connection between the pinch technique and the background field method is
further explored. We show by explicit calculations that the application of the
pinch technique in the framework of the background field method gives rise to
exactly the same results as in the linear renormalizable gauges. The general
method for extending the pinch technique to the case of Green's functions with
off-shell fermions as incoming particles is presented. As an example, the
one-loop gauge independent quark self-energy is constructed. We briefly discuss
the possibility that the gluonic Green's functions, obtained by either method,
correspond to physical quantities.Comment: 13 pages and 3 figures, all included in a uuencoded file, to appear
in Physical Review

### Fixed points and vacuum energy of dynamically broken gauge theories

We show that if a gauge theory with dynamical symmetry breaking has
non-trivial fixed points, they will correspond to extrema of the vacuum energy.
This relationship provides a different method to determine fixed points.Comment: 17 pages, uuencoded latex file, 3 figures, uses epsf and epsfig.
Submitted to Mod. Phys. Lett.

### Relativistic center-vortex dynamics of a confining area law

We offer a physicists' proof that center-vortex theory requires the area in
the Wilson-loop area law to involve an extremal area. Area-law dynamics is
determined by integrating over Wilson loops only, not over surface fluctuations
for a fixed loop. Fluctuations leading to to perimeter-law corrections come
from loop fluctuations as well as integration over finite -thickness
center-vortex collective coordinates. In d=3 (or d=2+1) we exploit a contour
form of the extremal area in isothermal which is similar to d=2 (or d=1+1) QCD
in many respects, except that there are both quartic and quadratic terms in the
action. One major result is that at large angular momentum \ell in d=3+1 the
center-vortex extremal-area picture yields a linear Regge trajectory with Regge
slope--string tension product \alpha'(0)K_F of 1/(2\pi), which is the canonical
Veneziano/string value. In a curious effect traceable to retardation, the quark
kinetic terms in the action vanish relative to area-law terms in the large-\ell
limit, in which light-quark masses \sim K_F^{1/2} are negligible. This
corresponds to string-theoretic expectations, even though we emphasize that the
extremal-area law is not a string theory quantum-mechanically. We show how some
quantum trajectory fluctuations as well as non-leading classical terms for
finite mass yield corrections scaling with \ell^{-1/2}. We compare to old
semiclassical calculations of relativistic q\bar{q} bound states at large \ell,
which also yield asymptotically-linear Regge trajectories, finding agreement
with a naive string picture (classically, not quantum-mechanically) and
disagreement with an effective-propagator model. We show that contour forms of
the area law can be expressed in terms of Abelian gauge potentials, and relate
this to old work of Comtet.Comment: 20 pages RevTeX4 with 3 .eps figure

### Effects of turbulence on a kinetic auroral arc model

A plasma kinetic model of an inverted-V auroral arc structure which includes the effects of electrostatic turbulence is proposed. In the absence of turbulence, a parallel potential drop is supported by magnetic mirror forces and charge quasi neutrality, with energetic auroral ions penetrating to low altitudes; relative to the electrons, the ions' pitch angle distribution is skewed toward smaller pitch angles. The electrons energized by the potential drop form a current which excites electrostatic turbulence. In equilibrium the plasma is marginally stable. The conventional anomalous resistivity contribution to the potential drop is very small. Anomalous resistivity processes are far too dissipative to be powered by auroral particles. It is concluded that under certain circumstances equilibrium may be impossible and relaxation oscillations set in

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