3,067 research outputs found
On the Integrable Structure of the Ising Model
Starting from the lattice realization of the Ising model defined on a
strip with integrable boundary conditions, the exact spectrum (including
excited states) of all the local integrals of motion is derived in the
continuum limit by means of TBA techniques. It is also possible to follow the
massive flow of this spectrum between the UV conformal fixed point and
the massive IR theory. The UV expression of the eigenstates of such integrals
of motion in terms of Virasoro modes is found to have only rational
coefficients and their fermionic representation turns out to be simply related
to the quantum numbers describing the spectrum.Comment: 18 pages, no figure
Exact conserved quantities on the cylinder II: off-critical case
With the aim of exploring a massive model corresponding to the perturbation
of the conformal model [hep-th/0211094] the nonlinear integral equation for a
quantum system consisting of left and right KdV equations coupled on the
cylinder is derived from an integrable lattice field theory. The eigenvalues of
the energy and of the transfer matrix (and of all the other local integrals of
motion) are expressed in terms of the corresponding solutions of the nonlinear
integral equation. The analytic and asymptotic behaviours of the transfer
matrix are studied and given.Comment: enlarged version before sending to jurnal, second part of
hep-th/021109
From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ
Initially, we derive a nonlinear integral equation for the vacuum counting
function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus
paralleling similar results by Kl\"umper \cite{KLU}, achieved through a
different technique in the {\it antiferroelectric regime}. In terms of the
counting function we obtain the usual physical quantities, like the energy and
the transfer matrix (eigenvalues). Then, we introduce a double scaling limit
which appears to describe the sine-Gordon theory on cylindrical geometry, so
generalising famous results in the plane by Luther \cite{LUT} and Johnson et
al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to
excitations, we derive scattering amplitudes involving solitons/antisolitons
first, and bound states later. The latter case comes out as manifestly related
to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this
nonlinear integral equations framework was contrived to deal with finite
geometries, we prove it to be effective for discovering or rediscovering
S-matrices. As a particular example, we prove that this unique model furnishes
explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe}
and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description
of unknown integrable field theories.Comment: Article, 41 pages, Late
Exact conserved quantities on the cylinder I: conformal case
The nonlinear integral equations describing the spectra of the left and right
(continuous) quantum KdV equations on the cylinder are derived from integrable
lattice field theories, which turn out to allow the Bethe Ansatz equations of a
twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear
integral equation of the twisted continuous spin chain is found. The
diagonalization of the transfer matrix is performed. The vacua sector is
analysed in detail detecting the primary states of the minimal conformal models
and giving integral expressions for the eigenvalues of the transfer matrix.
Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and
Zamolodchikov is realised. General expressions for the eigenvalues of the
infinite-dimensional abelian algebra of local integrals of motion are given and
explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe
TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
We consider high spin, , long twist, , planar operators (asymptotic
Bethe Ansatz) of strong SYM. Precisely, we compute the minimal
anomalous dimensions for large 't Hooft coupling to the lowest order
of the (string) scaling variable with GKP string size . At the leading order ,
we can confirm the O(6) non-linear sigma model description for this bulk term,
without boundary term . Going further, we derive,
extending the O(6) regime, the exact effect of the size finiteness. In
particular, we compute, at all loops, the first Casimir correction (in terms of the infinite size O(6) NLSM), which reveals only one
massless mode (out of five), as predictable once the O(6) description has been
extended. Consequently, upon comparing with string theory expansion, at one
loop our findings agree for large twist, while reveal for negligible twist,
already at this order, the appearance of wrapping. At two loops, as well as for
next loops and orders, we can produce predictions, which may guide future
string computations.Comment: Version 2 with: new exact expression for the Casimir energy derived
(beyond the first two loops of the previous version); UV theory formulated
and analysed extensively in the Appendix C; origin of the O(6) NLSM
scattering clarified; typos correct and references adde
Connected components of Morse boundaries of graphs of groups
Let a finitely generated group split as a graph of groups. If edge groups are undistorted and do not contribute to the Morse boundary , we show that every connected component of with at least two points originates from the Morse boundary of a vertex group. Under stronger assumptions on the edge groups (such as wideness in the sense of Dru\c{t}u-Sapir), we show that Morse boundaries of vertex groups are topologically embedded in
From the braided to the usual Yang-Baxter relation
Quantum monodromy matrices coming from a theory of two coupled (m)KdV
equations are modified in order to satisfy the usual Yang-Baxter relation. As a
consequence, a general connection between braided and {\it unbraided} (usual)
Yang-Baxter algebras is derived and also analysed.Comment: 13 Latex page
Culture of human cell lines by a pathogen-inactivated human platelet lysate
Alternatives to the use of fetal bovine serum (FBS) have been investigated to ensure xeno-free growth condition. In this study we evaluated the efficacy of human platelet lysate (PL) as a substitute of FBS for the in vitro culture of some human cell lines. PL was obtained by pools of pathogen inactivated human donor platelet (PLT) concentrates. Human leukemia cell lines (KG-1, K562, JURKAT, HL-60) and epithelial tumor cell lines (HeLa and MCF-7) were cultured with either FBS or PL. Changes in cell proliferation, viability, morphology, surface markers and cell cycle were evaluated for each cell line. Functional characteristics were analysed by drug sensitivity test and cytotoxicity assay. Our results demonstrated that PL can support growth and expansion of all cell lines, although the cells cultured in presence of PL experienced a less massive proliferation compared to those grown with FBS. We found a comparable percentage of viable specific marker-expressing cells in both conditions, confirming lineage fidelity in all cultures. Functionality assays showed that cells in both FBS- and PL-supported cultures maintained their normal responsiveness to adriamycin and NK cell-mediated lysis. Our findings indicate that PL is a feasible serum substitute for supporting growth and propagation of haematopoietic and epithelial cell lines with many advantages from a perspective of process standardization, ethicality and product safety
Equitable allocation of extrarenal organs: With special reference to the liver
A national plan is proposed for the equitable allocation of extrarenal organs, with particular reference to the liver. The principles of the plan include preferential use of the organs in the local and regional area of procurement, with national listing of the organs left over after the original cut. At each of the local, regional, and national levels, the allocation is based on total points awarded for medical urgency, time waiting, blood group conformity, and physical location of both donor and recipient. The plan, which should be applicable as well for allocation of hearts, is compatible with international sharing with nearby countries such as Canada
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