1,329 research outputs found
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
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
A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD
The Schrodinger wave functional for the d=3+1 SU(N) vacuum is a partition
function constructed in d=4; the exponent 2S in the square of the wave
functional plays the role of a d=3 Euclidean action. We start from a
gauge-invariant conjecture for the infrared-dominant part of S, based on
dynamical generation of a gluon mass M in d=4. We argue that the exact leading
term, of O(M), in an expansion of S in inverse powers of M is a d=3
gauge-invariant mass term (gauged non-linear sigma model); the next leading
term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is
the sum of these two terms has center vortices as classical solutions. The d=3
gluon mass, which we constrain to be the same as M, and d=3 coupling are
related through the conjecture to the d=4 coupling strength, but at the same
time the dimensionless ratio in d=3 of mass to coupling squared can be
estimated from d=3 dynamics. This allows us to estimate the QCD coupling
in terms of this strictly d=3 ratio; we find a value of about
0.4, in good agreement with an earlier theoretical value but a little low
compared to QCD phenomenology. The wave functional for d=2+1 QCD has an
exponent that is a d=2 infrared-effective action having both the
gauge-invariant mass term and the field strength squared term, and so differs
from the conventional QCD action in two dimensions, which has no mass term.
This conventional d=2 QCD would lead in d=3 to confinement of all color-group
representations. But with the mass term (again leading to center vortices),
N-ality = 0 mod N representations are not confined.Comment: 15 pages, no figures, revtex
Computing the Effective Hamiltonian of Low-Energy Vacuum Gauge Fields
A standard approach to investigate the non-perturbative QCD dynamics is
through vacuum models which emphasize the role played by specific gauge field
fluctuations, such as instantons, monopoles or vortexes. The effective
Hamiltonian describing the dynamics of the low-energy degrees of freedom in
such approaches is usually postulated phenomenologically, or obtained through
uncontrolled approximations. In a recent paper, we have shown how lattice field
theory simulations can be used to rigorously compute the effective Hamiltonian
of arbitrary vacuum models by stochastically performing the path integral over
all the vacuum field fluctuations which are not explicitly taken into account.
In this work, we present the first illustrative application of such an approach
to a gauge theory and we use it to compute the instanton size distribution in
SU(2) gluon-dynamics in a fully model independent and parameter-free way.Comment: 10 pages, 4 figure
On topological charge carried by nexuses and center vortices
In this paper we further explore the question of topological charge in the
center vortex-nexus picture of gauge theories. Generally, this charge is
locally fractionalized in units of 1/N for gauge group SU(N), but globally
quantized in integral units. We show explicitly that in d=4 global topological
charge is a linkage number of the closed two-surface of a center vortex with a
nexus world line, and relate this linkage to the Hopf fibration, with homotopy
; this homotopy insures integrality of the global
topological charge. We show that a standard nexus form used earlier, when
linked to a center vortex, gives rise naturally to a homotopy , a homotopy usually associated with 't Hooft-Polyakov monopoles and similar
objects which exist by virtue of the presence of an adjoint scalar field which
gives rise to spontaneous symmetry breaking. We show that certain integrals
related to monopole or topological charge in gauge theories with adjoint
scalars also appear in the center vortex-nexus picture, but with a different
physical interpretation. We find a new type of nexus which can carry
topological charge by linking to vortices or carry d=3 Chern-Simons number
without center vortices present; the Chern-Simons number is connected with
twisting and writhing of field lines, as the author had suggested earlier. In
general, no topological charge in d=4 arises from these specific static
configurations, since the charge is the difference of two (equal) Chern-Simons
number, but it can arise through dynamic reconnection processes. We complete
earlier vortex-nexus work to show explicitly how to express globally-integral
topological charge as composed of essentially independent units of charge 1/N.Comment: Revtex4; 3 .eps figures; 18 page
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
On a class of embeddings of massive Yang-Mills theory
A power-counting renormalizable model into which massive Yang-Mills theory is
embedded is analyzed. The model is invariant under a nilpotent BRST
differential s. The physical observables of the embedding theory, defined by
the cohomology classes of s in the Faddeev-Popov neutral sector, are given by
local gauge-invariant quantities constructed only from the field strength and
its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the
journa
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
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