1,347 research outputs found
Dynamical mass generation in quantum field theory : some methods with application to the Gross-Neveu model and Yang-Mills theory
We introduce some techniques to investigate dynamical mass generation. The
Gross-Neveu model (GN) is used as a toy model, because the GN mass gap is
exactly known, making it possible to check reliability of the various methods.
Very accurate results are obtained. Also application to SU(N) Yang-Mills (YM)
is discussed.Comment: 8 LaTeX2e pages, uses Kluwer class file crckbked.cls. Kluwer package
included. To appear in: Proceedings of the NATO Advanced Research Workshop on
"Confinement, Topology, and other Non-Perturbative Aspects of QCD", Stara
Lesna, Slovakia, 21-27 jan 200
Pair Interaction Potentials of Colloids by Extrapolation of Confocal Microscopy Measurements of Collective Structure
A method for measuring the pair interaction potential between colloidal
particles by extrapolation measurement of collective structure to infinite
dilution is presented and explored using simulation and experiment. The method
is particularly well suited to systems in which the colloid is fluorescent and
refractive index matched with the solvent. The method involves characterizing
the potential of mean force between colloidal particles in suspension by
measurement of the radial distribution function using 3D direct visualization.
The potentials of mean force are extrapolated to infinite dilution to yield an
estimate of the pair interaction potential, . We use Monte Carlo (MC)
simulation to test and establish our methodology as well as to explore the
effects of polydispersity on the accuracy. We use poly-12-hydroxystearic
acid-stabilized poly(methyl methacrylate) (PHSA-PMMA) particles dispersed in
the solvent dioctyl phthalate (DOP) to test the method and assess its accuracy
for three different repulsive systems for which the range has been manipulated
by addition of electrolyte.Comment: 35 pages, 14 figure
Modifying the Sum Over Topological Sectors and Constraints on Supergravity
The standard lore about the sum over topological sectors in quantum field
theory is that locality and cluster decomposition uniquely determine the sum
over such sectors, thus leading to the usual theta-vacua. We show that without
changing the local degrees of freedom, a theory can be modified such that the
sum over instantons should be restricted; e.g. one should include only
instanton numbers which are divisible by some integer p. This conclusion about
the configuration space of quantum field theory allows us to carefully
reconsider the quantization of parameters in supergravity. In particular, we
show that FI-terms and nontrivial Kahler forms are quantized. This analysis
also leads to a new derivation of recent results about linearized supergravity.Comment: 17 pages, minor change
Thermal phases of D1-branes on a circle from lattice super Yang-Mills
We report on the results of numerical simulations of 1+1 dimensional SU(N)
Yang-Mills theory with maximal supersymmetry at finite temperature and
compactified on a circle. For large N this system is thought to provide a dual
description of the decoupling limit of N coincident D1-branes on a circle. It
has been proposed that at large N there is a phase transition at strong
coupling related to the Gregory-Laflamme (GL) phase transition in the
holographic gravity dual. In a high temperature limit there was argued to be a
deconfinement transition associated to the spatial Polyakov loop, and it has
been proposed that this is the continuation of the strong coupling GL
transition. Investigating the theory on the lattice for SU(3) and SU(4) and
studying the time and space Polyakov loops we find evidence supporting this. In
particular at strong coupling we see the transition has the parametric
dependence on coupling predicted by gravity. We estimate the GL phase
transition temperature from the lattice data which, interestingly, is not yet
known directly in the gravity dual. Fine tuning in the lattice theory is
avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified
for clarity. v3: Normalisation of lattice coupling corrected by factor of two
resulting in change of estimate for c_cri
Random volumes from matrices
We propose a class of models which generate three-dimensional random volumes,
where each configuration consists of triangles glued together along multiple
hinges. The models have matrices as the dynamical variables and are
characterized by semisimple associative algebras A. Although most of the
diagrams represent configurations which are not manifolds, we show that the set
of possible diagrams can be drastically reduced such that only (and all of the)
three-dimensional manifolds with tetrahedral decompositions appear, by
introducing a color structure and taking an appropriate large N limit. We
examine the analytic properties when A is a matrix ring or a group ring, and
show that the models with matrix ring have a novel strong-weak duality which
interchanges the roles of triangles and hinges. We also give a brief comment on
the relationship of our models with the colored tensor models.Comment: 33 pages, 31 figures. Typos correcte
A Matrix Model for Baryons and Nuclear Forces
We propose a new matrix model describing multi-baryon systems. We derive the
action from open string theory on the wrapped baryon vertex D-branes embedded
in the D4-D8 model of large N holographic QCD. The positions of k baryons are
unified into k x k matrices, with spin/isospin of the baryons encoded in a set
of k-vectors. Holographic baryons are known to be very small in the large 't
Hooft coupling limit, and our model offers a better systematic approach to
dynamics of such baryons at short distances. We compute energetics and spectra
(k=1), and also short-distance nuclear force (k=2). In particular, we obtain a
new size of the holographic baryon and find a precise form of the repulsive
core of nucleons. This matrix model complements the instanton soliton picture
of holographic baryons, whose small size turned out to be well below the
natural length scale of the approximation involved there. Our results show
that, nevertheless, the basic properties of holographic baryons obtained there
are robust under stringy corrections within a few percents.Comment: 30 pages. v3: more comments added, published versio
Anomaly Equations and Intersection Theory
Six-dimensional supergravity theories with N=(1,0) supersymmetry must satisfy
anomaly equations. These equations come from demanding the cancellation of
gravitational, gauge and mixed anomalies. The anomaly equations have
implications for the geometrical data of Calabi-Yau threefolds, since F-theory
compactified on an elliptically fibered Calabi-Yau threefold with a section
generates a consistent six-dimensional N=(1,0) supergravity theory. In this
paper, we show that the anomaly equations can be summarized by three
intersection theory identities. In the process we also identify the geometric
counterpart of the anomaly coefficients---in particular, those of the abelian
gauge groups---that govern the low-energy dynamics of the theory. We discuss
the results in the context of investigating string universality in six
dimensions.Comment: 29 pages + appendices, 8 figures; v2: minor corrections, references
added; v3: minor corrections, reference adde
Renormalization group approach to matrix models via noncommutative space
We develop a new renormalization group approach to the large-N limit of
matrix models. It has been proposed that a procedure, in which a matrix model
of size (N-1) \times (N-1) is obtained by integrating out one row and column of
an N \times N matrix model, can be regarded as a renormalization group and that
its fixed point reveals critical behavior in the large-N limit. We instead
utilize the fuzzy sphere structure based on which we construct a new map
(renormalization group) from N \times N matrix model to that of rank N-1. Our
renormalization group has great advantage of being a nice analog of the
standard renormalization group in field theory. It is naturally endowed with
the concept of high/low energy, and consequently it is in a sense local and
admits derivative expansions in the space of matrices. In construction we also
find that our renormalization in general generates multi-trace operators, and
that nonplanar diagrams yield a nonlocal operation on a matrix, whose action is
to transport the matrix to the antipode on the sphere. Furthermore the
noncommutativity of the fuzzy sphere is renormalized in our formalism. We then
analyze our renormalization group equation, and Gaussian and nontrivial fixed
points are found. We further clarify how to read off scaling dimensions from
our renormalization group equation. Finally the critical exponent of the model
of two-dimensional gravity based on our formalism is examined.Comment: 1+42 pages, 4 figure
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