129 research outputs found
Conformal Field Theories, Representations and Lattice Constructions
An account is given of the structure and representations of chiral bosonic
meromorphic conformal field theories (CFT's), and, in particular, the
conditions under which such a CFT may be extended by a representation to form a
new theory. This general approach is illustrated by considering the untwisted
and -twisted theories, and respectively,
which may be constructed from a suitable even Euclidean lattice .
Similarly, one may construct lattices and by
analogous constructions from a doubly-even binary code . In the case when
is self-dual, the corresponding lattices are also. Similarly,
and are self-dual if and only if is. We show that
has a natural ``triality'' structure, which induces an
isomorphism and also a triality
structure on . For the Golay code,
is the Leech lattice, and the triality on is the symmetry which extends the natural action of (an
extension of) Conway's group on this theory to the Monster, so setting triality
and Frenkel, Lepowsky and Meurman's construction of the natural Monster module
in a more general context. The results also serve to shed some light on the
classification of self-dual CFT's. We find that of the 48 theories
and with central charge 24 that there are 39 distinct ones,
and further that all 9 coincidences are accounted for by the isomorphism
detailed above, induced by the existence of a doubly-even self-dual binary
code.Comment: 65 page
Single measurement to predict potential mineralizable nitrogen
Non-Peer ReviewedAlthough soil nitrate nitrogen (N) has been used as a basis for N fertilizer recommendation in western Canada, potential mineralizable N should be (or is) a more accurate indicator of the N supplying power of the soil. Potential mineralizable N, analyzed by extraction with hot KCl, and organic matter content were determined on the AESA Soil Quality Benchmark Sites in Alberta. Using these results, we developed an approach to estimate Nt from soil organic matter, based on the equation Nt=No(1-e-kt)y, and validated the calculated Nt with the hot KCl extracted N. Results indicated that the potential mineralizable N released from soil differed among ecoregions and slope positions. Potential mineralizable N is lower in southern Alberta than central Alberta. The lower slopes released more N than higher slope positions. Nt released in soil over the growing season correlated well with hot KCl extracted N in three different slope positions.
However, variability of Nt in the upper slope position was greater than middle and lower slopes due to a shallow A horizon and variable soil moisture during the growing season. After removal of outliers (9% of the total data set), the values of R2 (regression of hot KCl with calculated Nt) are 0.529, 0.576 and 0.627 for upper, middle and lower slope position, respectively. Using calculated Nt results, a potential mineralizable map in Alberta has been developed. This map will guide producers to manage soil as well as fertilizer N
The structure of parafermion vertex operator algebras
It is proved that the parafermion vertex operator algebra associated to the
irreducible highest weight module for the affine Kac-Moody algebra A_1^{(1)} of
level k coincides with a certain W-algebra. In particular, a set of generators
for the parafermion vertex operator algebra is determined.Comment: 12 page
The charges of a twisted brane
The charges of the twisted D-branes of certain WZW models are determined. The
twisted D-branes are labelled by twisted representations of the affine algebra,
and their charge is simply the ground state multiplicity of the twisted
representation. It is shown that the resulting charge group is isomorphic to
the charge group of the untwisted branes, as had been anticipated from a
K-theory calculation. Our arguments rely on a number of non-trivial Lie
theoretic identities.Comment: 27 pages, 1 figure, harvmac (b
Fluctuating Elastic Rings: Statics and Dynamics
We study the effects of thermal fluctuations on elastic rings. Analytical
expressions are derived for correlation functions of Euler angles, mean square
distance between points on the ring contour, radius of gyration, and
probability distribution of writhe fluctuations. Since fluctuation amplitudes
diverge in the limit of vanishing twist rigidity, twist elasticity is essential
for the description of fluctuating rings. We find a crossover from a small
scale regime in which the filament behaves as a straight rod, to a large scale
regime in which spontaneous curvature is important and twist rigidity affects
the spatial configurations of the ring. The fluctuation-dissipation relation
between correlation functions of Euler angles and response functions, is used
to study the deformation of the ring by external forces. The effects of inertia
and dissipation on the relaxation of temporal correlations of writhe
fluctuations, are analyzed using Langevin dynamics.Comment: 43 pages, 9 Figure
Spinons and parafermions in fermion cosets
We introduce a set of gauge invariant fermion fields in fermionic coset
models and show that they play a very central role in the description of
several Conformal Field Theories (CFT's). In particular we discuss the explicit
realization of primaries and their OPE in unitary minimal models, parafermion
fields in CFT's and that of spinon fields in
Wess-Zumino-Witten models (WZW) theories. The higher level case () will be
briefly discussed. Possible applications to QHE systems and spin-ladder systems
are addressed.Comment: 6 pages, Latex file. Invited talk at International Seminar dedicated
to the memory of D.V.Volkov, Kharkov, January 5-7, 199
Twisted boundary states in c=1 coset conformal field theories
We study the mutual consistency of twisted boundary conditions in the coset
conformal field theory G/H. We calculate the overlap of the twisted boundary
states of G/H with the untwisted ones, and show that the twisted boundary
states are consistently defined in the diagonal modular invariant. The overlap
of the twisted boundary states is expressed by the branching functions of a
twisted affine Lie algebra. As a check of our argument, we study the diagonal
coset theory so(2n)_1 \oplus so(2n)_1/so(2n)_2, which is equivalent with the
orbifold S^1/\Z_2. We construct the boundary states twisted by the
automorphisms of the unextended Dynkin diagram of so(2n), and show their mutual
consistency by identifying their counterpart in the orbifold. For the triality
of so(8), the twisted states of the coset theory correspond to neither the
Neumann nor the Dirichlet boundary states of the orbifold and yield the
conformal boundary states that preserve only the Virasoro algebra.Comment: 44 pages, 1 figure; (v2) minor change in section 2.3, references
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Kac-Moody algebras in perturbative string theory
The conjecture that M-theory has the rank eleven Kac-Moody symmetry e11
implies that Type IIA and Type IIB string theories in ten dimensions possess
certain infinite dimensional perturbative symmetry algebras that we determine.
This prediction is compared with the symmetry algebras that can be constructed
in perturbative string theory, using the closed string analogues of the DDF
operators. Within the limitations of this construction close agreement is
found. We also perform the analogous analysis for the case of the closed
bosonic string.Comment: 31 pages, harvmac (b), 4 eps-figure
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
On the Deformation of Dendrites During Directional Solidification of a Nickel-Based Superalloy
Abstract: Synchrotron X-ray imaging has been used to examine in situ the deformation of dendrites that takes place during the solidification of a nickel-based superalloy. By combining absorption and diffraction contrast imaging, deformation events could be classified by their localization and permanence. In particular, a deformation mechanism arising from thermal contraction in a temperature gradient was elucidated through digital image correlation. It was concluded that this mechanism may explain the small misorientations typically observed in single crystal castings
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