164 research outputs found
Exact beta function from the holographic loop equation of large-N QCD_4
We construct and study a previously defined quantum holographic effective
action whose critical equation implies the holographic loop equation of large-N
QCD_4 for planar self-avoiding loops in a certain regularization scheme. We
extract from the effective action the exact beta function in the given scheme.
For the Wilsonean coupling constant the beta function is exacly one loop and
the first coefficient agrees with its value in perturbation theory. For the
canonical coupling constant the exact beta function has a NSVZ form and the
first two coefficients agree with their value in perturbation theory.Comment: 42 pages, latex. The exponent of the Vandermonde determinant in the
quantum effective action has been changed, because it has been employed a
holomorphic rather than a hermitean resolution of identity in the functional
integral. Beta function unchanged. New explanations and references added,
typos correcte
Yang-Mills mass gap at large-N, non-commutative YM theory, topological quantum field theory and hyperfiniteness
We review a number of old and new concepts in quantum gauge theories, some of
which are well established but not widely appreciated, some are most recent.
Such concepts involve non-commutative gauge theories and their relation to the
large-N limit, loop equations and the change to the anti-selfdual variables
also known as Nicolai map, topological field theory (TFT) and its relation to
localization and Morse-Smale-Floer homology, with an emphasis both on the
mathematical aspects and the physical meaning. These concepts, assembled in a
new way, enter a line of attack to the problem of the mass gap in large-N SU(N)
YM, that is reviewed as well. In the large-N limit of pure SU(N) YM the ambient
algebra of Wilson loops is known to be a type II_1 non-hyperfinite factor.
Nevertheless, for the mass gap problem at the leading 1/N order, only the
subalgebra of local gauge-invariant single-trace operators matters. The
connected two-point correlators in this subalgebra must be an infinite sum of
propagators of free massive fields, a vast simplification. It is an open
problem, determined by the grow of the degeneracy of the spectrum, whether the
aforementioned local subalgebra is in fact hyperfinite. For the mass-gap
problem, in the search of a hyperfinite subalgebra containing the scalar sector
of large-N YM, a major role is played by the existence of a TFT underlying the
large-N limit of YM, with twisted boundary conditions on a torus or, what is
the same by Morita duality, on a non-commutative torus.Comment: 19 pages, latex; the paper, originally a byproduct of the workshop:
Mathematical Foundations of Quantum Field Theory, Jan 16-20 (2012), has been
expanded and rewritten as a short review in order to include most recent
developments. To appear in IJMP
âSoccer is a matter of real men?â Sexist and homophobic attitudes in three Italian soccer teams differentiated by sexual orientation and gender identity
During the 1980s and early 1990s, homophobia and sexism were pervasive in sport contexts due to their sex-segregation, male-domination, and heteronormative culture. In the last two decades, a change in attitudes toward gender and sexuality, in particular within typically masculine sports, has been observed. Notwithstanding that, no research assessing if this change also occurred in Italy was conducted. Using semi-structured focus groups and adopting the framework of Inclusive Masculinity Theory, the current study explored sexist and homophobic attitudes in three Italian soccer teams differentiated by gender and sexual orientation. Team 1 comprised openly gay male athletes, Team 2 comprised both lesbian and heterosexual women, and Team 3 comprised heterosexual men. Narratives were analysed through constant comparison analysis. Specific macro-categories were identified in each team, as follows: Team 1: need for affiliation, in/visibility, perceived homophobia, and perceived institutionalised homophobia; Team 2: need for affiliation, masculine dominance, equal opportunities, and crossing gender boundaries; and Team 3: presumption of heterosexuality, female inferiority, and tendency toward a homosocial law. The results suggest that soccer, in Italy, still represents a context organised around menâs dominance over women and the stigmatisation of gay men. Notwithstanding, they suggest also that we are witnessing an interlocutory phase where some heterosexual soccer players are starting to challenge homophobia but, at the same time, women and openly gay players still perceive a homohysteric culture. The discussion is contextualised in the social context where discourses arose
Twisted local systems solve the (holographic) loop equation of large-N QCD_4
We construct a holographic map from the loop equation of large-N QCD in d=2
and d=4, for planar self-avoiding loops, to the critical equation of an
equivalent effective action. The holographic map is based on two ingredients:
an already proposed holographic form of the loop equation, such that the
quantum contribution is reduced to a regularized residue; a new conformal map
from the region encircled by the based loop to a cuspidal fundamental domain in
the upper half-plane, such that the regularized residue vanishes at the cusp.
As a check, we study the first coefficient of the beta function and that part
of the second coefficient which arises from the rescaling anomaly, in passing
from the Wilsonian to the canonically normalised (holographic) effective
action.Comment: 42 pages, latex; abstract shortened and a reference added as
suggested by the referee; typos in Eq.(72,76,77,82,83,84) correcte
Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory
We localize the loop equation of large-N YM theory in the ASD variables on a
critical equation for an effective action by means of homological methods as
opposed to the cohomological localization of equivariantly closed forms in
local field theory. Our localization occurs for some special simple quasi BPS
Wilson loops, that have no perimeter divergence and no cusp anomaly for
backtracking cusps, in a partial Eguchi-Kawai reduction from four to two
dimensions of the non-commutative theory in the limit of infinite
non-commutativity and in a lattice regularization in which the ASD integration
variables live at the points of the lattice, thus implying an embedding of
parabolic Higgs bundles in the YM functional integral. We find that the beta
function of the effective action is saturated by the non-commutative ASD
vortices of the EK reduction. An exact canonical beta function of NSVZ type
that reproduces the universal first and second perturbative coefficients
follows by the localization on vortices. Finally we argue that a scheme can be
found in which the canonical coupling coincides with the physical charge
between static quark sources in the large-N limit and we compare our
theoretical calculation with some numerical lattice result.Comment: 52 pages, latex; a change of notation in the vortices equations; a
footnote adde
Entanglement Measures for Single- and Multi-Reference Correlation Effects
Electron correlation effects are essential for an accurate ab initio
description of molecules. A quantitative a priori knowledge of the single- or
multi-reference nature of electronic structures as well as of the dominant
contributions to the correlation energy can facilitate the decision regarding
the optimum quantum chemical method of choice. We propose concepts from quantum
information theory as orbital entanglement measures that allow us to evaluate
the single- and multi-reference character of any molecular structure in a given
orbital basis set. By studying these measures we can detect possible artifacts
of small active spaces.Comment: 14 pages, 4 figure
Heavy Baryon Specroscopy from the Lattice
The results of an exploratory lattice study of heavy baryon spectroscopy are
presented. We have computed the full spectrum of the eight baryons containing a
single heavy quark, on a lattice at , using an
-improved fermion action. We discuss the lattice baryon operators and
give a method for isolating the contributions of the spin doublets
, and to the correlation
function of the relevant operator. We compare our results with the available
experimental data and find good agreement in both the charm and the beauty
sectors, despite the long extrapolation in the heavy quark mass needed in the
latter case. We also predict the masses of several undiscovered baryons. We
compute the \Lambda-\mbox{pseudoscalar meson} and mass
splittings. Our results, which have errors in the range , are in good
agreement with the experimental numbers. For the mass
splitting, we find results considerably smaller than the experimental values
for both the charm and the beauty baryons, although in the latter case the
experimental results are still preliminary. This is also the case for the
lattice results for the hyperfine splitting for the heavy mesons.Comment: 31 pages LaTex, with postscript figures include
Light Hadron Spectrum and Quark Masses from Quenched Lattice QCD
We present details of simulations for the light hadron spectrum in quenched
QCD carried out on the CP-PACS parallel computer. Simulations are made with the
Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112
lattices at four lattice spacings (a \approx 0.1-0.05 fm) and the spatial
extent of 3 fm. Hadronic observables are calculated at five quark masses
(m_{PS}/m_V \approx 0.75 - 0.4), assuming the u and d quarks being degenerate
but treating the s quark separately. We find that the presence of quenched
chiral singularities is supported from an analysis of the pseudoscalar meson
data. We take m_\pi, m_\rho and m_K (or m_\phi) as input. After chiral and
continuum extrapolations, the agreement of the calculated mass spectrum with
experiment is at a 10% level. In comparison with the statistical accuracy of
1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates
a failure of the quenched approximation for the hadron spectrum: the meson
hyperfine splitting is too small, and the octet masses and the decuplet mass
splittings are both smaller than experiment. Light quark masses are calculated
using two definitions: the conventional one and the one based on the
axial-vector Ward identity. The two results converge toward the continuum
limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends
on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV
from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_\phi, indicating again a
failure of the quenched approximation. We obtain \Lambda_{\bar{MS}}^{(0)}=
219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the
pseudoscalar meson decay constants.Comment: 60 pages, 49 figure
Heavy Quark Spectroscopy and Matrix Elements: A Lattice Study using the Static Approximation
We present results of a lattice analysis of the parameter, , the
decay constant , and several mass splittings using the static
approximation. Results were obtained for 60 quenched gauge configurations
computed at on a lattice size of . Light quark
propagators were calculated using the -improved Sheikholeslami-Wohlert
action. We find \Bbstat(m_b) = 0.69\er{3}{4} {\rm(stat)}\er{2}{1}
{\rm(syst)}, corresponding to \Bbstat = 1.02\er{5}{6}\er{3}{2}, and \fbstat
= 266\err{18}{20}\err{28}{27} \mev, f_{B_s}^2 B_{B_s}/f_B^2 B_B =
1.34\er{9}{8}\er{5}{3}, where a variational fitting technique was used to
extract \fbstat. For the mass splittings we obtain M_{B_s}-M_{B_d} =
87\err{15}{12}\err{6}{12} \mev, M_{\Lambda_b}-M_{B_d} =
420\errr{100}{90}\err{30}{30} \mev and M_{B^*}^2-M_B^2 =
0.281\err{15}{16}\err{40}{37} \gev^2. We compare different smearing techniques
intended to improve the signal/noise ratio. From a detailed assessment of
systematic effects we conclude that the main systematic uncertainties are
associated with the renormalisation constants relating a lattice matrix element
to its continuum counterpart. The dependence of our findings on lattice
artefacts is to be investigated in the future.Comment: 40 pages, uuencoded compressed tar file, containing one LaTeX file
and 14 postscript files (to be included with epsf). Minor change in the value
of the B parameter. Contains corrected value for the B*-B mass splitting.
Version accepted for publication in Phys. Rev.
Solving loop equations by Hitchin systems via holography in large-N QCD_4
For (planar) closed self-avoiding loops we construct a "holographic" map from
the loop equations of large-N QCD_4 to an effective action defined over
infinite rank Hitchin bundles. The effective action is constructed densely
embedding Hitchin systems into the functional integral of a partially quenched
or twisted Eguchi-Kawai model, by means of the resolution of identity into the
gauge orbits of the microcanonical ensemble and by changing variables from the
moduli fields of Hitchin systems to the moduli of the corresponding holomorphic
de Rham local systems. The key point is that the contour integral that occurs
in the loop equations for the de Rham local systems can be reduced to the
computation of a residue in a certain regularization. The outcome is that, for
self-avoiding loops, the original loop equations are implied by the critical
equation of an effective action computed in terms of the localisation
determinant and of the Jacobian of the change of variables to the de Rham local
systems. We check, at lowest order in powers of the moduli fields, that the
localisation determinant reproduces exactly the first coefficient of the beta
function.Comment: 65 pages, late
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