228 research outputs found

### Vertices and the CJT Effective Potential

The Cornwall-Jackiw-Tomboulis effective potential is modified to include a
functional dependence on the fermion-gauge particle vertex, and applied to a
quark confining model of chiral symmetry breaking.Comment: 10 pages (latex), PURD-TH-93-1

### 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

### 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
$\Pi_3(S^3)\simeq Z$; 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 $\Pi_2(S^2)\simeq
Z$, 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

### 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

### Infrared behaviour of the pressure in g\phi^3 theory in 6 dimensions

In an earlier paper Almeida and Frenkel considered the calculation of the
pressure in g\phi^3 theory in 6 dimensions via the Schwinger--Dyson equation.
They found, under certain approximations, that a finite result ensues in the
infrared limit. We find this conclusion to remain true with certain variations
of these approximations, suggesting the finiteness of the result to be fairly
robust.Comment: 6 pages, 4 figures, uses revtex

### Non-linear Dynamics in QED_3 and Non-trivial Infrared Structure

In this work we consider a coupled system of Schwinger-Dyson equations for
self-energy and vertex functions in QED_3. Using the concept of a
semi-amputated vertex function, we manage to decouple the vertex equation and
transform it in the infrared into a non-linear differential equation of
Emden-Fowler type. Its solution suggests the following picture: in the absence
of infrared cut-offs there is only a trivial infrared fixed-point structure in
the theory. However, the presence of masses, for either fermions or photons,
changes the situation drastically, leading to a mass-dependent non-trivial
infrared fixed point. In this picture a dynamical mass for the fermions is
found to be generated consistently. The non-linearity of the equations gives
rise to highly non-trivial constraints among the mass and effective (`running')
gauge coupling, which impose lower and upper bounds on the latter for dynamical
mass generation to occur. Possible implications of this to the theory of
high-temperature superconductivity are briefly discussed.Comment: 29 pages LATEX, 7 eps figures incorporated, uses axodraw style.
Discussion on the massless case (section 2) modified; no effect on
conclusions, typos correcte

### Renormalized Wick expansion for a modified PQCD

The renormalization scheme for the Wick expansion of a modified version of
the perturbative QCD introduced in previous works is discussed. Massless QCD is
considered, by implementing the usual multiplicative scaling of the gluon and
quark wave functions and vertices. However, also massive quark and gluon
counter-terms are allowed in this mass less theory since the condensates are
expected to generate masses. A natural set of expansion parameters of the
physical quantities is introduced: the coupling itself and to masses $m_q$ and
$m_g$ associated to quarks and gluons respectively. This procedure allows to
implement a dimensional transmutation effect through these new mass scales. A
general expression for the new generating functional in terms of the mass
parameters $m_q$ and $m_g$ is obtained in terms of integrals over arbitrary but
constant gluon or quark fields in each case. Further, the one loop potential,
is evaluated in more detail in the case when only the quark condensate is
retained. This lowest order result again indicates the dynamical generation of
quark condensates in the vacuum.Comment: 13 pages, one figur

### $B\to \phi \pi$ and $B^0 \to \phi\phi$ in the Standard Model and new bounds on R parity violation

We study the pure penguin decays $B \to \phi\pi$ and $B^0 \to \phi\phi$.
Using QCD factorization, we find ${\cal B}(B^\pm \to\phi\pi^{\pm}
)=2.0^{+0.3}_{-0.1}\times 10^{-8}$. For the pure penguin annihilation process
$B^0 \to \phi\phi$, analyzed here for the first time, ${\cal B}(B^0
\to\phi\phi)=2.1^{+1.6}_{-0.3}\times 10^{-9}$. The smallness of these decays in
the Standard Model makes them sensitive probes for new physics. From the upper
limit of $B\to \phi\pi$,we find constraints on R parity violating couplings, $|
\lambda{''}_{i23}\lambda{''}_{i21}|<6\times10^{-5}$, $|
\lambda'_{i23}\lambda'_{i21}|<4\times10^{-4}$ and $|
\lambda'_{i32}\lambda'_{i12}|<4\times10^{-4}$ for $i=1,2,3$. Our new bounds on
$|\lambda{''}_{i23}\lambda{''}_{i21}|$ are one order of magnitude stronger than
before. Within the available upper bounds for $|
\lambda{''}_{i23}\lambda{''}_{i21}|$, $|\lambda'_{i23}\lambda'_{i21}|$ and
$|\lambda'_{i32}\lambda'_{i12}|$, we find that ${\cal B}(B\to\phi\phi)$ could
be enhanced to $10^{-8}\sim 10^{-7}$. Experimental searches for these decays
are strongly urged.Comment: 5 pages, 3 figures embede

### Cancellation of the Chiral Anomaly in a Model with Spontaneous Symmetry Breaking

A perturbatively renormalized Abelian Higgs-Kibble model with a chirally
coupled fermion is considered. The Slavnov identity is fulfilled to all orders
of perturbation theory, which is crucial for renormalizability in models with
vector bosons. BRS invariance, i.e. the validity of the identity, forces the
chiral anomaly to be cancelled by Wess-Zumino counterterms. This procedure
preserves the renormalizability in the one-loop approximation but it violates
the Froissart bounds for partial wave amplitudes above some energy and destroys
renormalizability from the second order in h bar onwards due to the
counterterms. (The paper has 3 figs. in postscript which are not included; send
request to the author's e-mailbox with subject: figures . The author is willing
to mail hard copies of the paper.)Comment: 13 pages, plain TeX, SI 92-1

### The Svetitsky-Yaffe conjecture for the plaquette operator

According to the Svetitsky-Yaffe conjecture, a (d+1)-dimensional pure gauge
theory undergoing a continuous deconfinement transition is in the same
universality class as a d-dimensional statistical model with order parameter
taking values in the center of the gauge group. We show that the plaquette
operator of the gauge theory is mapped into the energy operator of the
statistical model. For d=2, this identification allows us to use conformal
field theory techniques to evaluate exactly the correlation functions of the
plaquette operator at the critical point. In particular, we can evaluate
exactly the plaquette expectation value in presence of static sources, which
gives some new insight in the structure of the color flux tube in mesons and
baryons.Comment: 8 pages, LaTeX file + three .eps figure

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