20,287 research outputs found
Matrix Models, Argyres-Douglas singularities and double scaling limits
We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level
superpotential whose matrix model spectral curve develops an A_{n+1}
Argyres-Douglas singularity. We evaluate the coupling constants of the
low-energy U(1)^n theory and show that the large N expansion is singular at the
Argyres-Douglas points. Nevertheless, it is possible to define appropriate
double scaling limits which are conjectured to yield four dimensional
non-critical string theories as proposed by Ferrari. In the Argyres-Douglas
limit the n-cut spectral curve degenerates into a solution with n/2 cuts for
even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been
corrected and the calculation of the coupling constants of the low-energy
theory has been adde
Dynamical aspects of inextensible chains
In the present work the dynamics of a continuous inextensible chain is
studied. The chain is regarded as a system of small particles subjected to
constraints on their reciprocal distances. It is proposed a treatment of
systems of this kind based on a set Langevin equations in which the noise is
characterized by a non-gaussian probability distribution. The method is
explained in the case of a freely hinged chain. In particular, the generating
functional of the correlation functions of the relevant degrees of freedom
which describe the conformations of this chain is derived. It is shown that in
the continuous limit this generating functional coincides with a model of an
inextensible chain previously discussed by one of the authors of this work.
Next, the approach developed here is applied to a inextensible chain, called
the freely jointed bar chain, in which the basic units are small extended
objects. The generating functional of the freely jointed bar chain is
constructed. It is shown that it differs profoundly from that of the freely
hinged chain. Despite the differences, it is verified that in the continuous
limit both generating functionals coincide as it is expected.Comment: 15 pages, LaTeX 2e + various packages, 3 figures. The title has been
changed and three references have been added. A large part of the manuscript
has been rewritten to improve readability. Chapter 4 has been added. It
contains the construction of the generating functional without the
shish-kebab approximation and a new derivation of the continuous limit of the
freely jointed bar chai
On the asymmetric zero-range in the rarefaction fan
We consider the one-dimensional asymmetric zero-range process starting from a
step decreasing profile. In the hydrodynamic limit this initial condition leads
to the rarefaction fan of the associated hydrodynamic equation. Under this
initial condition and for totally asymmetric jumps, we show that the weighted
sum of joint probabilities for second class particles sharing the same site is
convergent and we compute its limit. For partially asymmetric jumps we derive
the Law of Large Numbers for the position of a second class particle under the
initial configuration in which all the positive sites are empty, all the
negative sites are occupied with infinitely many first class particles and with
a single second class particle at the origin. Moreover, we prove that among the
infinite characteristics emanating from the position of the second class
particle, this particle chooses randomly one of them. The randomness is given
in terms of the weak solution of the hydrodynamic equation through some sort of
renormalization function. By coupling the zero-range with the exclusion process
we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic
Large N and double scaling limits in two dimensions
Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper
self-contained, two figures and one appendix; v2: typos correcte
Bosonic Field Propagators on Algebraic Curves
In this paper we investigate massless scalar field theory on non-degenerate
algebraic curves. The propagator is written in terms of the parameters
appearing in the polynomial defining the curve. This provides an alternative to
the language of theta functions. The main result is a derivation of the third
kind differential normalized in such a way that its periods around the homology
cycles are purely imaginary. All the physical correlation functions of the
scalar fields can be expressed in terms of this object. This paper contains a
detailed analysis of the techniques necessary to study field theories on
algebraic curves. A simple expression of the scalar field propagator is found
in a particular case in which the algebraic curves have internal symmetry
and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma
Multivalued Fields on the Complex Plane and Conformal Field Theories
In this paper a class of conformal field theories with nonabelian and
discrete group of symmetry is investigated. These theories are realized in
terms of free scalar fields starting from the simple systems and scalar
fields on algebraic curves. The Knizhnik-Zamolodchikov equations for the
conformal blocks can be explicitly solved. Besides of the fact that one obtains
in this way an entire class of theories in which the operators obey a
nonstandard statistics, these systems are interesting in exploring the
connection between statistics and curved space-times, at least in the two
dimensional case.Comment: (revised version), 30 pages + one figure (not included), (requires
harvmac.tex), LMU-TPW 92-1
Chern-Simons Field Theories with Non-semisimple Gauge Group of Symmetry
Subject of this work is a class of Chern-Simons field theories with
non-semisimple gauge group, which may well be considered as the most
straightforward generalization of an Abelian Chern-Simons field theory. As a
matter of fact these theories, which are characterized by a non-semisimple
group of gauge symmetry, have cubic interactions like those of non-abelian
Chern-Simons field theories, but are free from radiative corrections. Moreover,
at the tree level in the perturbative expansion,there are only two connected
tree diagrams, corresponding to the propagator and to the three vertex
originating from the cubic interaction terms. For such theories it is derived
here a set of BRST invariant observables, which lead to metric independent
amplitudes. The vacuum expectation values of these observables can be computed
exactly. From their expressions it is possible to isolate the Gauss linking
number and an invariant of the Milnor type, which describes the topological
relations among three or more closed curves.Comment: 16 pages, 1 figure, plain LaTeX + psfig.st
Hydro-mechanichal characterisation of bentonite/steel interfaces
The hydromechanical response of a Wyoming-type bentonite (MX-80) and its interface with steel was studied in terms of shear resistance under different hydration levels. A series of shear tests under constant normal stress were performed in total suction controlled conditions. In the case of bentonite samples, higher shear resistance was obtained for higher levels of applied suction. The shear properties of the bentonite/steel interface were overall lower than the internal properties of the bentonite, and they were not affected in a significant way by the hydration level. All samples presented a compactive response during shearing
A Monte Carlo approach to study neutron and fragment emission in heavy-ion reactions
Quantum Molecular Dynamics models (QMD) are Monte Carlo approaches targeted
at the description of nucleon-ion and ion-ion collisions. We have developed a
QMD code, which has been used for the simulation of the fast stage of ion-ion
collisions, considering a wide range of system masses and system mass
asymmetries. The slow stage of the collisions has been described by statistical
methods. The combination of both stages leads to final distributions of
particles and fragments, which have been compared to experimental data
available in literature. A few results of these comparisons, concerning neutron
double-differential production cross-sections for C, Ne and Ar ions impinging
on C, Cu and Pb targets at 290 - 400 MeV/A bombarding energies and fragment
isotopic distributions from Xe + Al at 790 MeV/A, are shown in this paper.Comment: 12 pages, 3 figures, submitted for publication in Adv. Space Re
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