149 research outputs found
Symplectic fermions and a quasi-Hopf algebra structure on
We consider the (finite-dimensional) small quantum group at
. We show that does not allow for an R-matrix, even
though holds for all finite-dimensional
representations of . We then give an explicit
coassociator and an R-matrix such that becomes a
quasi-triangular quasi-Hopf algebra.
Our construction is motivated by the two-dimensional chiral conformal field
theory of symplectic fermions with central charge . There, a braided
monoidal category, , has been computed from the factorisation and
monodromy properties of conformal blocks, and we prove that
is braided monoidally equivalent to
.Comment: 40pp, 11 figures; v2: few very minor corrections for the final
version in Journal of Algebr
Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
For generic values of q, all the eigenvectors of the transfer matrix of the
U_q sl(2)-invariant open spin-1/2 XXZ chain with finite length N can be
constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin.
However, when q is a root of unity (q=exp(i pi/p) with integer p>1), the Bethe
equations acquire continuous solutions, and the transfer matrix develops Jordan
cells. Hence, there appear eigenvectors of two new types: eigenvectors
corresponding to continuous solutions (exact complete p-strings), and
generalized eigenvectors. We propose general ABA constructions for these two
new types of eigenvectors. We present many explicit examples, and we construct
complete sets of (generalized) eigenvectors for various values of p and N.Comment: 50pp, 2 figures, v2: few typos are fixed, Nucl. Phys. B (2016
Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of
finite length N. For the case that q is a root of unity, we propose a formula
for the number of admissible solutions of the Bethe ansatz equations in terms
of dimensions of irreducible representations of the Temperley-Lieb algebra; and
a formula for the degeneracies of the transfer matrix eigenvalues in terms of
dimensions of tilting sl(2)_q-modules. These formulas include corrections that
appear if two or more tilting modules are spectrum-degenerate. For the XX case
(q=exp(i pi/2)), we give explicit formulas for the number of admissible
solutions and degeneracies. We also consider the cases of generic q and the
isotropic (q->1) limit. Numerical solutions of the Bethe equations up to N=8
are presented. Our results are consistent with the Bethe ansatz solution being
complete.Comment: 34 pages; v2: reference added; v3: two more references added and
minor correction
Testing of QED: Natural broadening of spectral lines
The difficulties associated with surface divergences, of a consistent QED theory in describing of the natural broadening (NB) of atomic systems are studied. This problem seems to be clearly and sensetively (in experimental meaning) appeared in the case of heavy muhicharged ions. To overcome this difficulty we have used a quantity of elementary interaction length, an analogy of the length of coherence. We have obtained that the NB contains a linear 1-divergence besides of a logarifmic one arrising in standard QED calculations. A Z-dependence has allowed us to suggest earring out the experimental testing of QED in the highly ionised atoms with the aid of more accurate technologies
Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
We derive and study a quantum group g(p,q) that is Kazhdan--Lusztig-dual to
the W-algebra W(p,q) of the logarithmic (p,q) conformal field theory model. The
algebra W(p,q) is generated by two currents and of dimension
(2p-1)(2q-1), and the energy--momentum tensor T(z). The two currents generate a
vertex-operator ideal with the property that the quotient W(p,q)/R is the
vertex-operator algebra of the (p,q) Virasoro minimal model. The number (2 p q)
of irreducible g(p,q)-representations is the same as the number of irreducible
W(p,q)-representations on which acts nontrivially. We find the center of
g(p,q) and show that the modular group representation on it is equivalent to
the modular group representation on the W(p,q) characters and
``pseudocharacters.'' The factorization of the g(p,q) ribbon element leads to a
factorization of the modular group representation on the center. We also find
the g(p,q) Grothendieck ring, which is presumably the ``logarithmic'' fusion of
the (p,q) model.Comment: 52pp., AMSLaTeX++. half a dozen minor inaccuracies (cross-refs etc)
correcte
Some possible techniques for improving the strength characteristics of folded cores from sheet composite materials
We consider some general problems of improving the strength characteristics of folded cores as well as the corresponding techniques for modifying the core material polymer surfaces with the use of nanotechnologies and the "mass-strength" criteria. © Allerton Press, Inc., 2009
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