1,038 research outputs found
Open-closed field algebras
We introduce the notions of open-closed field algebra and open-closed field
algebra over a vertex operator algebra V. In the case that V satisfies certain
finiteness and reductivity conditions, we show that an open-closed field
algebra over V canonically gives an algebra over a \C-extension of the
Swiss-cheese partial operad. We also give a tensor categorical formulation and
categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few
references are adde
Lectures on conformal field theory and Kac-Moody algebras
This is an introduction to the basic ideas and to a few further selected
topics in conformal quantum field theory and in the theory of Kac-Moody
algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate
Course on Conformal Field Theory and Integrable Models (Budapest, August
1996), to appear in Springer Lecture Notes in Physic
Conformal Field Theories, Graphs and Quantum Algebras
This article reviews some recent progress in our understanding of the
structure of Rational Conformal Field Theories, based on ideas that originate
for a large part in the work of A. Ocneanu. The consistency conditions that
generalize modular invariance for a given RCFT in the presence of various types
of boundary conditions --open, twisted-- are encoded in a system of integer
multiplicities that form matrix representations of fusion-like algebras. These
multiplicities are also the combinatorial data that enable one to construct an
abstract ``quantum'' algebra, whose - and -symbols contain essential
information on the Operator Product Algebra of the RCFT and are part of a cell
system, subject to pentagonal identities. It looks quite plausible that the
classification of a wide class of RCFT amounts to a classification of ``Weak
- Hopf algebras''.Comment: 23 pages, 12 figures, LateX. To appear in MATHPHYS ODYSSEY 2001
--Integrable Models and Beyond, ed. M. Kashiwara and T. Miwa, Progress in
Math., Birkhauser. References and comments adde
Free boson formulation of boundary states in W_3 minimal models and the critical Potts model
We develop a Coulomb gas formalism for boundary conformal field theory having
a symmetry and illustrate its operation using the three state Potts model.
We find that there are free-field representations for six conserving
boundary states, which yield the fixed and mixed physical boundary conditions,
and two violating boundary states which yield the free and new boundary
conditions. Other violating boundary states can be constructed but they
decouple from the rest of the theory. Thus we have a complete free-field
realization of the known boundary states of the three state Potts model. We
then use the formalism to calculate boundary correlation functions in various
cases. We find that the conformal blocks arising when the two point function of
is calculated in the presence of free and new boundary conditions
are indeed the last two solutions of the sixth order differential equation
generated by the singular vector.Comment: 25 page
Model for Glass Transition in a Binary fluid from a Mode Coupling approach
We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary
fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a
proper choice of the slow variables corresponding to the conservation laws. The
resulting model equations are solved in the long time limit to locate the
dynamic transition. The transition point from our model is considerably higher
than predicted in existing MCT models for binary systems. This is in agreement
with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 Figure
Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results
Numerical renormalization group and conformal field theory work indicate that
the two impurity Kondo Hamiltonian has a non-Fermi liquid critical point
separating the Kondo-screening phase from the inter-impurity singlet phase when
particle-hole (P-H) symmetry is maintained. We clarify the circumstances under
which this critical point occurs, pointing out that there are two types of P-H
symmetry. Only one of them guarantees the occurance of the critical point. Much
of the previous numerical work was done on models with the other type of P-H
symmetry. We analyse this critical point using the boundary conformal field
theory technique. The finite-size spectrum is presented in detail and compared
with about 50 energy levels obtained using the numerical renormalization group.
Various Green's functions, general renormalization group behaviour, and a
hidden are analysed.Comment: 38 pages, RevTex. 2 new sections clarify the circumstances under
which a model will exhibit the non-trivial critical point (hence potentially
resolving disagreements with other Authors) and explain the hidden SO(7)
symmetry of the model, relating it to an alternative approach of Sire et al.
and Ga
Industrial applications of accelerator-based infrared sources: analysis using infrared microspectroscopy
Infrared Microspectroscopy, using a globar source, is now widely employed in the industrial environment, for the analysis of various materials. Since synchrotron radiation is a much brighter source, an enhancement of an order of magnitude in lateral resolution can be achieved. Thus, the combination of IR microspectroscopy and synchrotron radiation provides a powerful tool enabling sample regions only few microns size to be studied. This opens up the potential for analyzing small particles. Some examples for hair, bitumen and polymer are presented
Multispecies virial expansions
We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs
Cardy condition for open-closed field algebras
Let be a vertex operator algebra satisfying certain reductivity and
finiteness conditions such that , the category of V-modules, is
a modular tensor category. We study open-closed field algebras over V equipped
with nondegenerate invariant bilinear forms for both open and closed sectors.
We show that they give algebras over certain \C-extension of the Swiss-cheese
partial dioperad, and we obtain Ishibashi states easily in such algebras. We
formulate Cardy condition algebraically in terms of the action of the modular
transformation on the space of intertwining
operators. We then derive a graphical representation of S in the modular tensor
category . This result enables us to give a categorical
formulation of Cardy condition and modular invariant conformal full field
algebra over . Then we incorporate the modular invariance condition
for genus-one closed theory, Cardy condition and the axioms for open-closed
field algebra over V equipped with nondegenerate invariant bilinear forms into
a tensor-categorical notion called Cardy -algebra. We also give a categorical construction of Cardy
-algebra in Cardy case.Comment: 70 page, 105 figures, references are updated. less typos, to appear
in Comm. Math. Phy
Type IIB orientifolds on Gepner points
We study various aspects of orientifold projections of Type IIB closed string
theory on Gepner points in different dimensions. The open string sector is
introduced, in the usual constructive way, in order to cancel RR charges
carried by orientifold planes. Moddings by cyclic permutations of the internal
N=2 superconformal blocks as well as by discrete phase symmetries are
implemented. Reduction in the number of generations, breaking or enhancements
of gauge symmetries and topology changes are shown to be induced by such
moddings. Antibranes sector is also considered; in particular we show how non
supersymmetric models with antibranes and free of closed and open tachyons do
appear in this context. A systematic study of consistent models in D=8
dimensions and some illustrative examples in D=6 and D=4 dimensions are
presented.Comment: 67 pages, no figures References added, typos correcte
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