730 research outputs found
An Affine String Vertex Operator Construction at Arbitrary Level
An affine vertex operator construction at arbitrary level is presented which
is based on a completely compactified chiral bosonic string whose momentum
lattice is taken to be the (Minkowskian) affine weight lattice. This
construction is manifestly physical in the sense of string theory, i.e., the
vertex operators are functions of DDF ``oscillators'' and the Lorentz
generators, both of which commute with the Virasoro constraints. We therefore
obtain explicit representations of affine highest weight modules in terms of
physical (DDF) string states. This opens new perspectives on the representation
theory of affine Kac-Moody algebras, especially in view of the simultaneous
treatment of infinitely many affine highest weight representations of arbitrary
level within a single state space as required for the study of hyperbolic
Kac-Moody algebras. A novel interpretation of the affine Weyl group as the
``dimensional null reduction'' of the corresponding hyperbolic Weyl group is
given, which follows upon re-expression of the affine Weyl translations as
Lorentz boosts.Comment: 15 pages, LaTeX2e, packages amsfonts, amssymb, xspace; final version
to appear in J. Math. Phy
The Sugawara generators at arbitrary level
We construct an explicit representation of the Sugawara generators for
arbitrary level in terms of the homogeneous Heisenberg subalgebra, which
generalizes the well-known expression at level 1. This is achieved by employing
a physical vertex operator realization of the affine algebra at arbitrary
level, in contrast to the Frenkel--Kac--Segal construction which uses
unphysical oscillators and is restricted to level 1. At higher level, the new
operators are transcendental functions of DDF ``oscillators'' unlike the
quadratic expressions for the level-1 generators. An essential new feature of
our construction is the appearance, beyond level 1, of new types of poles in
the operator product expansions in addition to the ones at coincident points,
which entail (controllable) non-localities in our formulas. We demonstrate the
utility of the new formalism by explicitly working out some higher-level
examples. Our results have important implications for the problem of
constructing explicit representations for higher-level root spaces of
hyperbolic Kac--Moody algebras, and in particular.Comment: 17 pages, 1 figure, LaTeX2e, amsfonts, amssymb, xspace, PiCTe
Missing Modules, the Gnome Lie Algebra, and
We study the embedding of Kac-Moody algebras into Borcherds (or generalized
Kac-Moody) algebras which can be explicitly realized as Lie algebras of
physical states of some completely compactified bosonic string. The extra
``missing states'' can be decomposed into irreducible highest or lowest weight
``missing modules'' w.r.t. the relevant Kac-Moody subalgebra; the corresponding
lowest weights are associated with imaginary simple roots whose multiplicities
can be simply understood in terms of certain polarization states of the
associated string. We analyse in detail two examples where the momentum lattice
of the string is given by the unique even unimodular Lorentzian lattice
or , respectively. The former leads to the Borcherds
algebra , which we call ``gnome Lie algebra", with maximal Kac-Moody
subalgebra . By the use of the denominator formula a complete set of
imaginary simple roots can be exhibited, whereas the DDF construction provides
an explicit Lie algebra basis in terms of purely longitudinal states of the
compactified string in two dimensions. The second example is the Borcherds
algebra , whose maximal Kac-Moody subalgebra is the hyperbolic algebra
. The imaginary simple roots at level 1, which give rise to irreducible
lowest weight modules for , can be completely characterized;
furthermore, our explicit analysis of two non-trivial level-2 root spaces leads
us to conjecture that these are in fact the only imaginary simple roots for
.Comment: 31 pages, LaTeX2e, AMS packages, PSTRICK
E10 for beginners
Invited talk presented by H. Nicolai at the Feza GĂĽrsey Memorial Conference, Istanbul, June 1994
E10 for beginners - Contribution to GĂĽrsey Memorial Conference Proceedings '94
We present a nontechnical introduction to the hyperbolic Kac Moody algebra E_{10} and summarize our recent attempt to understand the root spaces of Kac Moody algebras of hyperbolic type in terms of a DDF construction appropriate to a subcritical compactified bosonic string
On the fundamental representation of Borcherds algebras with one imaginary simple root
Borcherds algebras represent a new class of Lie algebras which have almost
all the properties that ordinary Kac-Moody algebras have, and the only major
difference is that these generalized Kac-Moody algebras are allowed to have
imaginary simple roots. The simplest nontrivial examples one can think of are
those where one adds ``by hand'' one imaginary simple root to an ordinary
Kac-Moody algebra. We study the fundamental representation of this class of
examples and prove that an irreducible module is given by the full tensor
algebra over some integrable highest weight module of the underlying Kac-Moody
algebra. We also comment on possible realizations of these Lie algebras in
physics as symmetry algebras in quantum field theory.Comment: 8 page
Damage-free single-mode transmission of deep-UV light in hollow-core PCF
Transmission of UV light with high beam quality and pointing stability is
desirable for many experiments in atomic, molecular and optical physics. In
particular, laser cooling and coherent manipulation of trapped ions with
transitions in the UV require stable, single-mode light delivery. Transmitting
even ~2 mW CW light at 280 nm through silica solid-core fibers has previously
been found to cause transmission degradation after just a few hours due to
optical damage. We show that photonic crystal fiber of the kagom\'e type can be
used for effectively single-mode transmission with acceptable loss and bending
sensitivity. No transmission degradation was observed even after >100 hours of
operation with 15 mW CW input power. In addition it is shown that
implementation of the fiber in a trapped ion experiment significantly increases
the coherence times of the internal state transfer due to an increase in beam
pointing stability
Changes in extracellular pH during electrical stimulation of isolated rat vagus nerve
Double-barrelled pH-sensitive micro-electrodes were used to record changes of extracellular pH during repetitive stimulation of isolated rat vagus nerves. It was found that a small initial alkaline shift was followed by a prolonged acidification. The acidification was correlated in time with the poststimulus undershoot of the extracellular K+ activity and with the recovery phase of the nerve conduction velocity. In the presence of ouabain, the acid component of the pH change was completely abolished (indicating a metabolic origin), whereas the alkaline component remained unaltered. These pH changes were too small to make a significant contribution to the activity-related changes in conduction velocity of the vagal C-fibres
Top Management Team Diversity: A systematic Review
Empirical research investigating the impact of top management team (TMT)
diversity on executives’ decision making has produced inconclusive results.
To synthesize and aggregate the results on the diversity-performance
link, a meta-regression analysis (MRA) is conducted. It integrates more
than 200 estimates from 53 empirical studies investigating TMT diversity
and its impact on the quality of executives’ decision making as reflected
in corporate performance. The analysis contributes to the literature by
theoretically discussing and empirically examining the effects of TMT diversity
on corporate performance. Our results do not show a link between TMT
diversity and performance but provide evidence for publication bias. Thus,
the findings raise doubts on the impact of TMT diversity on performance
Is the classical Bukhvostov-Lipatov model integrable? A Painlev\'e analysis
In this work we apply the Weiss, Tabor and Carnevale integrability criterion
(Painlev\'e analysis) to the classical version of the two dimensional
Bukhvostov-Lipatov model. We are led to the conclusion that the model is not
integrable classically, except at a trivial point where the theory can be
described in terms of two uncoupled sine-Gordon models
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