6,720 research outputs found

### Vacuum energy as a c-function for theories with dynamically generated masses

We argue that in asymptotically free non-Abelian gauge theories possessing
the phenomenon of dynamical mass generation the $\beta$ function is negative up
to a value of the coupling constant that corresponds to a non-trivial fixed
point, in agreement with recent AdS/QCD analysis. This fixed point happens at
the minimum of the vacuum energy ($\Omega$), which, as a characteristic of
theories with dynamical mass generation, has the properties of a c-function.Comment: 12 pages, 3 figure

### 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

### Baryonic hybrids: Gluons as beads on strings between quarks

We analyze the ground state of the heavy-quark hybrid system composed of
three quarks and a gluon. The known string tension K and approximately-known
gluon mass M lead to a precise specification of the long-range non-relativistic
part of the potential binding the gluon to the quarks with no undetermined
phenomenological parameters, in the limit of large interquark separation R. Our
major tool (also used earlier by Simonov) is the use of proper-time methods to
describe gluon propagation within the quark system, which reveals the gluon
Wilson line as a composite of co-located quark and antiquark lines. We show
that (aside from color-Coulomb and similar terms) the gluon potential energy in
the presence of quarks is accurately described via attaching these three
strings to the gluon, which in equilibrium sits at the middle of the Y-shaped
string network joining the three quarks. The gluon undergoes small harmonic
fluctuations that slightly stretch these strings and quasi-confine the gluon to
the neighborhood of the middle. In the non-relativistic limit (large R) we use
the Schrodinger equation, ignoring mixing with l=2 states. Relativistic
corrections (smaller R) are applied with a variational principle for the
relativistic harmonic oscillator. We also consider the role of color-Coulomb
contributions. We find leading non-relativistic large-R terms in the gluon
string energy which behave like the square root of K/(MR). The relativistic
energy goes like the cube root of K/R. We get an acceptable fit to lattice data
with M = 500 MeV. We show that in the quark-antiquark hybrid the gluon is a
bead that can slide without friction on a string joining the quark and
anti-quark. We comment briefly on the significance of our findings to
fluctuations of the minimal surface.Comment: 18 pages, revtex4 plus 8 .eps figures in one .tar.gz fil

### Three easy exercises in off-shell string-inspired methods

Off-shell string-inspired methods (OSSIM) calculate off-shell QCD Green's
functions using Schwinger-Feynman proper-time techniques, always in the
background field method (BFM) Feynman gauge for technical convenience, and so
far only at one loop. We already know that these results are gauge-invariant,
because this gauge realizes the prescriptions of the Pinch Technique (PT), a
Feynman-graph formulation for any gauge, but the idea of the first exercise is
to show this directly in OSSIM. In this exercise we extend proper-time OSSIM
beyond the BFM Feynman gauge so that one can apply PT algorithms, and show that
the intrinsic PT is equivalent to resolving ambiguities in OSSIM in other
gauges. In the second exercise we use forty-year-old rules of the author and
Tiktopoulos for expressing loop integrals with numerator momenta directly in
terms of Feynman parameters after momentum integration (the goal of OSSIM) and
show that these rules elegantly and with economy of effort give rise, at least
at one loop, to standard OSSIM algorithms. In the third exercise we apply
world-line techniques to the problem of the breaking of adjoint strings,
requiring a non-perturbative treatment that in the end reduces to a variant of
the Schwinger result for production of electron-positron pairs in an electric
field. This generalizes OSSIM to non-perturbative processes.Comment: 12 pages, 3 figures, talk given at "From quarks and gluons to
hadronic matter: A bridge too far?"[QCD-TNT-III], Trento, Italy, Sept. 2-6,
201

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