1,870 research outputs found
Eigenvalue Distributions of the QCD Dirac Operator
We compute by Monte Carlo methods the individual distributions of the th
smallest Dirac operator eigenvalues in QCD, and compare them with recent
analytical predictions. We do this for both massless and massive quarks in an
SU(3) gauge theory with staggered fermions. Very precise agreement is found in
all cases. As a simple by-product we also extract the microscopic spectral
density of the Dirac operator in SU(3) gauge theory with dynamical massive
fermions for and 2, and obtain high-accuracy agreement with analytical
expressions.Comment: LaTeX, 8 pages, 9 postscript figures. Very minor correction
Smooth Non-Abelian Bosonization
We present an extension of ``smooth bosonization'' to the non-Abelian case.
We construct an enlarged theory containing both bosonic and fermionic fields
which exhibits a local chiral gauge symmetry. A gauge fixing function depending
on one real parameter allows us to interpolate smoothly between a purely
fermionic and a purely bosonic representation. The procedure is, in the special
case of bosonization, complementary to the approach based on duality.Comment: LaTeX, 13 pages, CERN--TH-7347/9
Looking for Effects of Topology in the Dirac Spectrum of Staggered Fermions
We classify SU(3) gauge field configurations in different topological sectors
by the smearing technique. In each sector we compute the distribution of low
lying eigenvalues of the staggered Dirac operator. In all sectors we find
perfect agreement with the predictions for the sector of topological charge
zero. The smallest Dirac operator eigenvalues of staggered fermions at
presently realistic lattice couplings are thus insensitive to gauge field
topology. On the smeared configurations, eigenvalues go to zero in
agreement with the index theorem.Comment: Poster at Lattice99(topology), 3 page
Qualitons from QCD
Qualitons, topological excitations with the quantum numbers of quarks, may
provide an accurate description of what is meant by constituent quarks in QCD.
Their existence hinges crucially on an effective Lagrangian description of QCD
in which a pseudoscalar colour-octet of fields enters as a new variable. We
show here how such new fields may be extracted from the fundamental QCD
Lagrangian using the gauge-symmetric collective field technique.Comment: LaTeX, 12 pages, CERN--TH-7073/9
The C-Theorem and Chiral Symmetry Breaking in Asymptotically Free Vectorlike Gauge Theories
We confront Cardy's suggested c-function for four-dimensional field theories
with the spontaneous breaking of chiral symmetries in asymptotically free
vectorlike gauge theories with fermions transforming according to different
representations under the gauge group. Assuming that the infrared limit of the
c-function is determined by the dimension of the associated Goldstone manifold,
we find that this c-function always decreases between the ultraviolet and
infrared fixed points.Comment: 8 pages, no figures, a few references adde
Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories
It has been conjectured that spontaneous chiral symmetry breaking in strongly
coupled vectorlike gauge theories falls into only three different classes,
depending on the gauge group and the representations carried by the fermions.
We test this proposal by studying SU(2), SU(3) and SU(4) lattice gauge theories
with staggered fermions in different irreducible representations. Staggered
fermions away from the continuum limit should, for all complex representations,
still belong to the continuum class of spontaneous symmetry breaking. But for
all real and pseudo-real representations we show that staggered fermions should
belong to incorrect symmetry breaking classes away from the continuum, thus
generalizing previous results. As an unambiguous signal for whether chiral
symmetry breaks, and which breaking pattern it follows, we look at the smallest
Dirac eigenvalue distributions. We find that the patterns of symmetry breaking
are precisely those conjectured.Comment: LaTeX, 17 pages. Typos in eq (17) correcte
Non abelian bosonisation in three dimensional field theory
We develop a method based on the generalised St\"uckelberg prescription for
discussing bosonisation in the low energy regime of the SU(2) massive Thirring
model in 2+1 dimensions. For arbitrary values of the coupling parameter the
bosonised theory is found to be a nonabelian gauge theory whose physical sector
is explicitly obtained. In the case of vanishing coupling this gauge theory can
be identified with the SU(2) Yang-Mills Chern-Simons theory in the limit when
the Yang-Mills term vanishes. Bosonisation identities for the fermionic current
are derived.Comment: Latex version, 14 pages; 23 reference
BRST Gauge Fixing and Regularization
In the presence of consistent regulators, the standard procedure of BRST
gauge fixing (or moving from one gauge to another) can require non-trivial
modifications. These modifications occur at the quantum level, and gauges exist
which are only well-defined when quantum mechanical modifications are correctly
taken into account. We illustrate how this phenomenon manifests itself in the
solvable case of two-dimensional bosonization in the path-integral formalism.
As a by-product, we show how to derive smooth bosonization in
Batalin-Vilkovisky Lagrangian BRST quantization.Comment: LaTeX, 12 page
Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
We compute the low-lying spectrum of the staggered Dirac operator above and
below the finite temperature phase transition in both quenched QCD and in
dynamical four flavor QCD. In both cases we find, in the high temperature
phase, a density with close to square root behavior, . In the quenched simulations we find, in addition, a
volume independent tail of small eigenvalues extending down to zero. In the
dynamical simulations we also find a tail, decreasing with decreasing mass, at
the small end of the spectrum. However, the tail falls off quite quickly and
does not seem to extend to zero at these couplings. We find that the
distribution of the smallest Dirac operator eigenvalues provides an efficient
observable for an accurate determination of the location of the chiral phase
transition, as first suggested by Jackson and Verbaarschot.Comment: LaTeX, 20 pages, 13 postscript figures. Reference added. To appear in
Nucl. Phys.
Collective Fields for QCD
A gauge-symmetric approach to effective Lagrangians is described with special
emphasis on derivations of effective low-energy Lagrangians from QCD. The
examples we discuss are based on exact rewritings of cut-off QCD in terms of
new collective degrees of freedom. These cut-off Lagrangians are thus
``effective'' in the sense that they explicitly contain some of the physical
long-distance degrees of freedom from the outset.(Talk presented by P.H.
Damgaard at the workshop on ``Quantum Field Theoretical Methods in High Energy
Physics'', Kyffhauser, Germany, Sept. 1993. To appear in those proceedings).Comment: LaTeX, 12 pages, CERN--TH-7035/9
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