1,700 research outputs found
On The Phase Transition in D=3 Yang-Mills Chern-Simons Gauge Theory
Yang-Mills theory in three dimensions, with a Chern-Simons term of
level (an integer) added, has two dimensionful coupling constants,
and ; its possible phases depend on the size of relative to . For
, 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 ,
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 , called , with . Three lines of evidence are given: First, a gauge-invariant one-loop
calculation shows that the perturbative theory has tachyonic problems if .The theory becomes sensible only if there is an additional dynamic
source of gauge-boson mass, just as in the case. Second, we study in a
rough approximation the free energy and show that for there is a
non-trivial vacuum condensate driven by soliton entropy and driving a
gauge-boson dynamical mass , while both the condensate and vanish for . Third, we study possible quantum solitons stemming from an effective
action having both a Chern-Simons mass and a (gauge-invariant) dynamical
mass . We show that if M \gsim 0.5 m, there are finite-action quantum
sphalerons, while none survive in the classical limit , as shown earlier
by D'Hoker and Vinet. There are also quantum topological vortices smoothly
vanishing as .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, 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
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 , where 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 ) of the form
, where R is the spacelike dimension of a rectangular Wilson
loop. The linear-regime slope is not necessarily related to 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
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.
A unified theory of stable auroral red arc formation at the plasmapause
A theory is proposed that SAR-arcs are generated at the plasmapause as a consequence of the turbulent dissipation of ring current energy. During the recovery phase of a geomagnetic storm, the plasmapause expands outward into the symmetric ring current. When the cold plasma densities reach about 100/cu cm, ring current protons become unstable and generate intense ion cyclotron wave turbulence in a narrow region 1/2 earth radius wide (just inside the plasmapause). Approximately one-half of the ring current energy is dissipated into wave turbulence which in turn is absorbed through a Landau resonant interaction with plasma spheric electrons. The combined thermal heat flux to the ionosphere due to Landau absorption of the wave energy and proton-electron Coulomb dissipation is sufficient to drive SAR-arcs at the observed intensities. It is predicted that the arcs should be localized to a narrow latitudinal range just within the stormtime plasmapause. They should occur at all local times and persist for the 10 to 20 hour duration of the plasma-pause expansion
The heavy quark decomposition of the S-matrix and its relation to the pinch technique
We propose a decomposition of the S-matrix into individually gauge invariant
sub-amplitudes, which are kinematically akin to propagators, vertices, boxes,
etc. This decompsition is obtained by considering limits of the S-matrix when
some or all of the external particles have masses larger than any other
physical scale. We show at the one-loop level that the effective gluon
self-energy so defined is physically equivalent to the corresponding gauge
independent self-energy obtained in the framework of the pinch technique. The
generalization of this procedure to arbitrary gluonic -point functions is
briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0
Baryon number non-conservation and phase transitions at preheating
Certain inflation models undergo pre-heating, in which inflaton oscillations
can drive parametric resonance instabilities. We discuss several phenomena
stemming from such instabilities, especially in weak-scale models; generically,
these involve energizing a resonant system so that it can evade tunneling by
crossing barriers classically. One possibility is a spontaneous change of phase
from a lower-energy vacuum state to one of higher energy, as exemplified by an
asymmetric double-well potential with different masses in each well. If the
lower well is in resonance with oscillations of the potential, a system can be
driven resonantly to the upper well and stay there (except for tunneling) if
the upper well is not resonant. Another example occurs in hybrid inflation
models where the Higgs field is resonant; the Higgs oscillations can be
transferred to electroweak (EW) gauge potentials, leading to rapid transitions
over sphaleron barriers and consequent B+L violation. Given an appropriate
CP-violating seed, we find that preheating can drive a time-varying condensate
of Chern-Simons number over large spatial scales; this condensate evolves by
oscillation as well as decay into modes with shorter spatial gradients,
eventually ending up as a condensate of sphalerons. We study these examples
numerically and to some extent analytically. The emphasis in the present paper
is on the generic mechanisms, and not on specific preheating models; these will
be discussed in a later paper.Comment: 10 pages, 7 figures included, revtex, epsf, references adde
Speculations on Primordial Magnetic Helicity
We speculate that above or just below the electroweak phase transition
magnetic fields are generated which have a net helicity (otherwise said, a
Chern-Simons term) of order of magnitude , where is the
baryon or lepton number today. (To be more precise requires much more knowledge
of B,L-generating mechanisms than we currently have.) Electromagnetic helicity
generation is associated (indirectly) with the generation of electroweak
Chern-Simons number through B+L anomalies. This helicity, which in the early
universe is some 30 orders of magnitude greater than what would be expected
from fluctuations alone in the absence of B+L violation, should be reasonably
well-conserved through the evolution of the universe to around the times of
matter dominance and decoupling, because the early universe is an excellent
conductor. Possible consequences include early structure formation; macroscopic
manifestations of CP violation in the cosmic magnetic field (measurable at
least in principle, if not in practice); and an inverse-cascade dynamo
mechanism in which magnetic fields and helicity are unstable to transfer to
larger and larger spatial scales. We give a quasi-linear treatment of the
general-relativistic MHD inverse cascade instability, finding substantial
growth for helicity of the assumed magnitude out to scales , where is roughly the B+L to photon ratio and
is the magnetic correlation length. We also elaborate further on an
earlier proposal of the author for generation of magnetic fields above the EW
phase transition.Comment: Latex, 23 page
Gauge Coupling Instability and Dynamical Mass Generation in N=1 Supersymmetric QED(3)
Using superfield Dyson-Schwinger equations, we compute the infrared dynamics
of the semi-amputated full vertex, corresponding to the effective running gauge
coupling, in N-flavour {\mathcal N}=1 supersymmetric QED(3). It is shown that
the presence of a supersymmetry-preserving mass for the matter multiplet
stabilizes the infrared gauge coupling against oscillations present in the
massless case, and we therefore infer that the massive vacuum is thus selected
at the level of the (quantum) effective action. We further demonstrate that
such a mass can indeed be generated dynamically in a self-consistent way by
appealing to the superfield Dyson-Schwinger gap equation for the full matter
propagator.Comment: 14 pages ReVTeX; four axodraw figures incorporate
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