185 research outputs found
Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity
We study the zeros in the complex plane of the partition function for the
Ising model coupled to 2d quantum gravity for complex magnetic field and real
temperature, and for complex temperature and real magnetic field, respectively.
We compute the zeros by using the exact solution coming from a two matrix model
and by Monte Carlo simulations of Ising spins on dynamical triangulations. We
present evidence that the zeros form simple one-dimensional curves in the
complex plane, and that the critical behaviour of the system is governed by the
scaling of the distribution of the singularities near the critical point.
Despite the small size of the systems studied, we can obtain a reasonable
estimate of the (known) critical exponents.Comment: 22 pages, LaTeX2e, 10 figures, added discussion on antiferromagnetic
transition and reference
Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes
It has been observed that in the DIS scheme the refactorization of the
Drell-Yan cross section leading to exponentiation of threshold logarithms can
also be used to organize a class of constant terms, most of which arise from
the ratio of the timelike Sudakov form factor to its spacelike counterpart. We
extend this exponentiation to include all constant terms, and demonstrate how a
similar organization may be achieved in the MSbar scheme. We study the
relevance of these exponentiations in a two-loop analysis.Comment: 20 pages, JHEP style, no figure
All-order results for soft and collinear gluons
I briefly review some general features and some recent developments
concerning the resummation of long-distance singularities in QCD and in more
general non-abelian gauge theories. I emphasize the field-theoretical tools of
the trade, and focus mostly on the exponentiation of infrared and collinear
divergences in amplitudes, which underlies the resummation of large logarithms
in the corresponding cross sections. I then describe some recent results
concerning the conformal limit, notably the case of N = 4 superymmetric
Yang-Mills theoryComment: 15 pages, invited talk presented at the 10th Workshop in High Energy
Physics Phenomenology (WHEPP X), Chennai, India, January 200
On soft singularities at three loops and beyond
We report on further progress in understanding soft singularities of massless
gauge theory scattering amplitudes. Recently, a set of equations was derived
based on Sudakov factorization, constraining the soft anomalous dimension
matrix of multi-leg scattering amplitudes to any loop order, and relating it to
the cusp anomalous dimension. The minimal solution to these equations was shown
to be a sum over color dipoles. Here we explore potential contributions to the
soft anomalous dimension that go beyond the sum-over-dipoles formula. Such
contributions are constrained by factorization and invariance under rescaling
of parton momenta to be functions of conformally invariant cross ratios.
Therefore, they must correlate the color and kinematic degrees of freedom of at
least four hard partons, corresponding to gluon webs that connect four eikonal
lines, which first appear at three loops. We analyze potential contributions,
combining all available constraints, including Bose symmetry, the expected
degree of transcendentality, and the singularity structure in the limit where
two hard partons become collinear. We find that if the kinematic dependence is
solely through products of logarithms of cross ratios, then at three loops
there is a unique function that is consistent with all available constraints.
If polylogarithms are allowed to appear as well, then at least two additional
structures are consistent with the available constraints.Comment: v2: revised version published in JHEP (minor corrections in Sec. 4;
added discussion in Sec. 5.3; refs. added); v3: minor corrections (eqs. 5.11,
5.12 and 5.29); 38 pages, 3 figure
Three-dimensional QCD in the adjoint representation and random matrix theory
In this paper we complete the derivations of finite volume partition
functions for QCD using random matrix theories by calculating the effective
low-energy partition function for three-dimensional QCD in the adjoint
representation from a random matrix theory with the same global symmetries. As
expected, this case corresponds to Dyson index , that is, the Dirac
operator can be written in terms of real quaternions. After discussing the
issue of defining Majorana fermions in Euclidean space, the actual matrix model
calculation turns out to be simple. We find that the symmetry breaking pattern
is , as expected from the correspondence
between symmetric (super)spaces and random matrix universality classes found by
Zirnbauer. We also derive the first Leutwyler--Smilga sum rule.Comment: LaTeX, 19 pages. Minor corrections, added comments, to appear on
Phys. Rev.
An infrared approach to Reggeization
We present a new approach to Reggeization of gauge amplitudes based on the
universal properties of their infrared singularities. Using the "dipole
formula", a compact ansatz for all infrared singularities of massless
amplitudes, we study Reggeization of singular contributions to high-energy
amplitudes for arbitrary color representations, and any logarithmic accuracy.
We derive leading-logarithmic Reggeization for general cross-channel color
exchanges, and we show that Reggeization breaks down for the imaginary part of
the amplitude at next-to-leading logarithms and for the real part at
next-to-next-to-leading logarithms. Our formalism applies to multiparticle
amplitudes in multi-Regge kinematics, and constrains possible corrections to
the dipole formula starting at three loops.Comment: 4 page
Rapidity gaps in perturbative QCD
We analyze diffractive deep inelastic scattering within perturbative QCD by
studying lepton scattering on a heavy quark target. Simple explicit expressions
are derived in impact parameter space for the photon wave function and the
scattering cross sections corresponding to single and double Coulomb gluon
exchange. At limited momentum transfers to the target, the results agree with
the general features of the ``aligned jet model''. The color--singlet exchange
cross section receives a leading twist contribution only from the aligned jet
region, where the transverse size of the photon wave function remains finite in
the Bjorken scaling limit. In contrast to inclusive DIS, in diffractive events
there is no leading twist contribution to from the lowest
order photon Fock state, and the cross section for heavy quarks is
power suppressed in the quark mass. There are also important contributions with
large momentum transfer to the target, which corresponds to events having high
transverse momentum production in both the projectile and target rapidity
regions, separated by a rapidity gap.Comment: 27 pages, LaTeX, 6 figures. Duplicate figure removed, paper unchange
Timelike form factors at high energy
The difference between the timelike and spacelike meson form factors is
analysed in the framework of perturbative QCD with Sudakov effects included. It
is found that integrable singularities appear but that the asymptotic behavior
is the same in the timelike and spacelike regions. The approach to asymptotia
is quite slow and a rather constant enhancement of the timelike value is
expected at measurable large . This is in agreement with the trend
shown by experimental data.Comment: 17 pages, report DAPNIA/SPhN 94 0
Quantum chromodynamics sub-group
This is the report of the QCD working sub-group at the Tenth Workshop on High Energy Physics Phenomenology (WHEPP-X)
Random matrices beyond the Cartan classification
It is known that hermitean random matrix ensembles can be identified with
symmetric coset spaces of Lie groups, or else with tangent spaces of the same.
This results in a classification of random matrix ensembles as well as
applications in practical calculations of physical observables. In this paper
we show that a large number of non-hermitean random matrix ensembles defined by
physically motivated symmetries - chiral symmetry, time reversal invariance,
space rotation invariance, particle-hole symmetry, or different reality
conditions - can likewise be identified with symmetric spaces. We give explicit
representations of the random matrix ensembles identified with lateral algebra
subspaces, and of the corresponding symmetric subalgebras spanning the group of
invariance. Among the ensembles listed we identify as special cases all the
hermitean ensembles identified with Cartan classes of symmetric spaces and the
three Ginibre ensembles with complex eigenvalues.Comment: 41 pages, no figures. References and comments added; the
representation of ensemble 15 changed to quaternion real. Version accepted
for publication on J. Phys.
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