12 research outputs found
Bailey flows and Bose-Fermi identities for the conformal coset models
We use the recently established higher-level Bailey lemma and Bose-Fermi
polynomial identities for the minimal models to demonstrate the
existence of a Bailey flow from to the coset models
where is a
positive integer and is fractional, and to obtain Bose-Fermi identities
for these models. The fermionic side of these identities is expressed in terms
of the fractional-level Cartan matrix introduced in the study of .
Relations between Bailey and renormalization group flow are discussed.Comment: 28 pages, AMS-Latex, two references adde
Local height probabilities in a composite Andrews-Baxter-Forrester model
We study the local height probabilities in a composite height model, derived
from the restricted solid-on-solid model introduced by Andrews, Baxter and
Forrester, and their connection with conformal field theory characters. The
obtained conformal field theories also describe the critical behavior of the
model at two different critical points. In addition, at criticality, the model
is equivalent to a one-dimensional chain of anyons, subject to competing two-
and three-body interactions. The anyonic-chain interpretation provided the
original motivation to introduce the composite height model, and by obtaining
the critical behaviour of the composite height model, the critical behaviour of
the anyonic chains is established as well. Depending on the overall sign of the
hamiltonian, this critical behaviour is described by a diagonal coset-model,
generalizing the minimal models for one sign, and by Fateev-Zamolodchikov
parafermions for the other.Comment: 34 pages, 5 figures; v2: expanded introduction, references added and
other minor change
Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
We present fermionic sum representations of the characters
of the minimal models for all relatively prime
integers for some allowed values of and . Our starting point is
binomial (q-binomial) identities derived from a truncation of the state
counting equations of the XXZ spin chain of anisotropy
. We use the Takahashi-Suzuki method to express
the allowed values of (and ) in terms of the continued fraction
decomposition of (and ) where stands for
the fractional part of These values are, in fact, the dimensions of the
hermitian irreducible representations of (and )
with (and We also establish the duality relation and discuss the action of the Andrews-Bailey transformation in the
space of minimal models. Many new identities of the Rogers-Ramanujan type are
presented.Comment: Several references, one further explicit result and several
discussion remarks adde
On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case
We consider the local field dynamical temperature correlation function of the
Quantum Nonlinear Schrodinger equation with the finite coupling constant. This
correlation function admits a Fredholm determinant representation. The related
operator-valued Riemann--Hilbert problem is used for analysing the leading term
of the large time and long distance asymptotics of the correlation function.Comment: 70 pages, Latex, 4 figure
Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4\nu)
We prove polynomial identities for the N=1 superconformal model SM(2,4\nu)
which generalize and extend the known Fermi/Bose character identities. Our
proof uses the q-trinomial coefficients of Andrews and Baxter on the bosonic
side and a recently introduced very general method of producing recursion
relations for q-series on the fermionic side. We use these polynomials to
demonstrate a dual relation under q \rightarrow q^{-1} between SM(2,4\nu) and
M(2\nu-1,4\nu). We also introduce a generalization of the Witten index which is
expressible in terms of the Rogers false theta functions.Comment: 41 pages, harvmac, no figures; new identities, proofs and comments
added; misprints eliminate
Thermodynamics and conformal properties of XXZ chains with alternating spins
The quantum periodic XXZ chain with alternating spins is studied. The
properties of the related R-matrix and Hamiltonians are discussed. A compact
expression for the ground state energy is obtained. The corresponding conformal
anomaly is found via the finite-size computations and also by means of the
Bethe ansatz method. In the presence of an external magnetic field, the
magnetic susceptibility is derived. The results are also generalized to the
case of a chain containing several different spins.Comment: 28 pages, LaTeX2
Calcium modulates force sensing by the von Willebrand factor A2 domain
von Willebrand factor (VWF) multimers mediate primary adhesion and aggregation of platelets. VWF potency critically depends on multimer size, which is regulated by a feedback mechanism involving shear-induced unfolding of the VWF-A2 domain and cleavage by the metalloprotease ADAMTS-13. Here we report crystallographic and single-molecule optical tweezers data on VWF-A2 providing mechanistic insight into calcium-mediated stabilization of the native conformation that protects A2 from cleavage by ADAMTS-13. Unfolding of A2 requires higher forces when calcium is present and primarily proceeds through a mechanically stable intermediate with non-native calcium coordination. Calcium further accelerates refolding markedly, in particular, under applied load. We propose that calcium improves force sensing by allowing reversible force switching under physiologically relevant hydrodynamic conditions. Our data show for the first time the relevance of metal coordination for mechanical properties of a protein involved in mechanosensing