1,728 research outputs found
Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model
The 7--particle form factors of the fundamental spin field of the O(3)
nonlinear --model are constructed. We calculate the corresponding
contribution to the spin--spin correlation function, and compare with
predictions from the spectral density scaling hypothesis. The resulting
approximation to the spin--spin correlation function agrees well with that
computed in renormalized (asymptotically free) perturbation theory in the
expected energy range. Further we observe simple lower and upper bounds for the
sum of the absolute square of the form factors which may be of use for analytic
estimates.Comment: 14 pages, 3 figures, late
Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
We study the universality between a discrete spin model with icosahedral
symmetry and the O(3) model in two dimensions. For this purpose we study
numerically the renormalized two-point functions of the spin field and the four
point coupling constant. We find that those quantities seem to have the same
continuum limits in the two models. This has far reaching consequences, because
the icosahedron model is not asymptotically free in the sense that the coupling
constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in
the short distance limit. By universality this then also applies to the O(3)
model, contrary to the predictions of perturbation theory.Comment: 18 pages, 8 figures Color coding in Fig. 5 changed to improve
visibilit
Comment on "Scaling Hypothesis for the Spectral Densities in the Nonlinear Sigma Model"
We comment on the recent paper by Balog and Niedermaier [hep-th/9701156].Comment: 3 page
On the Chiral WZNW Phase Space, Exchange r-Matrices and Poisson-Lie Groupoids
This is a review of recent work on the chiral extensions of the WZNW phase
space describing both the extensions based on fields with generic monodromy as
well as those using Bloch waves with diagonal monodromy. The symplectic form on
the extended phase space is inverted in both cases and the chiral WZNW fields
are found to satisfy quadratic Poisson bracket relations characterized by
monodromy dependent exchange r-matrices. Explicit expressions for the exchange
r-matrices in terms of the arbitrary monodromy dependent 2-form appearing in
the chiral WZNW symplectic form are given. The exchange r-matrices in the
general case are shown to satisfy a new dynamical generalization of the
classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are
constructed that encode this equation analogously as PL groups encode the
classical YB equation. For an arbitrary simple Lie group , exchange
r-matrices are exhibited that are in one-to-one correspondence with the
possible PL structures on and admit them as PL symmetries.Comment: Based on a lecture by L.F. at the Seminaire de Mathematiques
Superieures, Montreal, 1999; LaTeX, 21 page
Coadjoint orbits of the Virasoro algebra and the global Liouville equation
The classification of the coadjoint orbits of the Virasoro algebra is
reviewed and is then applied to analyze the so-called global Liouville
equation. The review is self-contained, elementary and is tailor-made for the
application. It is well-known that the Liouville equation for a smooth, real
field under periodic boundary condition is a reduction of the SL(2,R)
WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to
be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction
yields, for the field where is a constant,
what we call the global Liouville equation. Corresponding to the winding number
of the SL(2,R) WZNW model there is a topological invariant in the reduced
theory, given by the number of zeros of Q over a period. By the substitution
, the Liouville theory for a smooth is recovered in
the trivial topological sector. The nontrivial topological sectors can be
viewed as singular sectors of the Liouville theory that contain blowing-up
solutions in terms of . Since the global Liouville equation is
conformally invariant, its solutions can be described by explicitly listing
those solutions for which the stress-energy tensor belongs to a set of
representatives of the Virasoro coadjoint orbits chosen by convention. This
direct method permits to study the `coadjoint orbit content' of the topological
sectors as well as the behaviour of the energy in the sectors. The analysis
confirms that the trivial topological sector contains special orbits with
hyperbolic monodromy and shows that the energy is bounded from below in this
sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP
Dynamical r-matrices and the chiral WZNW phase space
The dynamical generalization of the classical Yang-Baxter equation that
governs the possible Poisson structures on the space of chiral WZNW fields with
generic monodromy is reviewed. It is explained that for particular choices of
the chiral WZNW Poisson brackets this equation reduces to the CDYB equation
recently studied by Etingof--Varchenko and others. Interesting dynamical
r-matrices are obtained for generic monodromy as well as by imposing Dirac
constraints on the monodromy.Comment: Talk given at XXIII International Colloquium on Group Theoretical
Methods in Physics, July 31 - August 5, 2000, Dubna, Russia. LaTeX, 9 page
An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term
A toy model is proposed for four dimensional non-abelian gauge theories
coupled to a large number of fermionic degrees of freedom. As the number of
flavors is varied the gauge theory may be confining, walking or conformal. The
toy model mimicking this feature is the two dimensional O(3) sigma model with a
theta-term. For all theta the model is asymptotically free. For small theta the
model is confining in the infra red, for theta = pi the model has a non-trivial
infra red fixed point and consequently for theta slightly below pi the coupling
walks. The first step in investigating the notoriously difficult systematic
effects of the gauge theory in the toy model is to establish non-perturbatively
that the theta parameter is actually a relevant coupling. This is done by
showing that there exist quantities that are entirely given by the total
topological charge and are well defined in the continuum limit and are
non-zero, despite the fact that the topological susceptibility is divergent.
More precisely it is established that the differences of connected correlation
functions of the topological charge (the cumulants) are finite and non-zero and
consequently there is only a single divergent parameter in Z(theta) but
otherwise it is finite. This divergent constant can be removed by an
appropriate counter term rendering the theory completely finite even at theta >
0.Comment: 9 pages, 2 figures, minor modification, references adde
The Chiral WZNW Phase Space and its Poisson-Lie Groupoid
The precise relationship between the arbitrary monodromy dependent 2-form
appearing in the chiral WZNW symplectic form and the `exchange r-matrix' that
governs the corresponding Poisson brackets is established. Generalizing earlier
results related to diagonal monodromy, the exchange r-matrices are shown to
satisfy a new dynamical generalization of the classical modified Yang-Baxter
equation, which is found to admit an interpretation in terms of (new)
Poisson-Lie groupoids. Dynamical exchange r-matrices for which right
multiplication yields a classical or a Poisson-Lie symmetry on the chiral WZNW
phase space are presented explicitly.Comment: 13 pages, LaTeX, minor typos correcte
Effects of different cultivation techniques on vineyard fauna
Green covering compared to soil cultivation enhanced the number of individuals of Araneae living on or near soil. No differences between the different soil management systems were found for the number of individuals of Staphylinidae and Carabidae. The typical main species of the two systems were different for all groups analyzed (Araneae, Staphylinidae and Carabidae)
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