1,772 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 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
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
Conical twist fields and null polygonal Wilson loops
Using an extension of the concept of twist field in QFT to space–time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon appropriate identification between the excess angle and the number of sheets, they have the same conformal dimension as branch-point twist fields commonly used to represent partition functions on Riemann surfaces, and that both fields have closely related form factors. However, we show that conical twist fields are truly different from branch-point twist fields. They generate different operator product expansions (short distance expansions) and form factor expansions (large distance expansions). In fact, we verify in free field theories, by re-summing form factors, that the conical twist fields operator product expansions are correctly reproduced. We propose that conical twist fields are the correct fields in order to understand null polygonal Wilson loops/gluon scattering amplitudes of planar maximally supersymmetric Yang–Mills theory
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
A braided Yang-Baxter Algebra in a Theory of two coupled Lattice Quantum KdV: algebraic properties and ABA representations
A generalization of the Yang-Baxter algebra is found in quantizing the
monodromy matrix of two (m)KdV equations discretized on a space lattice. This
braided Yang-Baxter equation still ensures that the transfer matrix generates
operators in involution which form the Cartan sub-algebra of the braided
quantum group. Representations diagonalizing these operators are described
through relying on an easy generalization of Algebraic Bethe Ansatz techniques.
The conjecture that this monodromy matrix algebra leads, {\it in the cylinder
continuum limit}, to a Perturbed Minimal Conformal Field Theory description is
analysed and supported.Comment: Latex file, 46 page
Scattering of Giant Holes
We study scalar excitations of high spin operators in N=4 super Yang-Mills
theory, which are dual to solitons propagating on a long folded string in AdS_3
x S^1. In the spin chain description of the gauge theory, these are associated
to holes in the magnon distribution in the sl(2,R) sector. We compute the
all-loop hole S-matrix from the asymptotic Bethe ansatz, and expand in leading
orders at weak and strong coupling. The worldsheet S-matrix of solitonic
excitations on the GKP string is calculated using semiclassical quantization.
We find an exact agreement between the gauge theory and string theory results.Comment: 13 pages. v2: minor corrections, references adde
The generalised scaling function: a systematic study
We describe a procedure for determining the generalised scaling functions
at all the values of the coupling constant. These functions describe
the high spin contribution to the anomalous dimension of large twist operators
(in the sector) of SYM. At fixed , can be
obtained by solving a linear integral equation (or, equivalently, a linear
system with an infinite number of equations), whose inhomogeneous term only
depends on the solutions at smaller . In other words, the solution can be
written in a recursive form and then explicitly worked out in the strong
coupling regime. In this regime, we also emphasise the peculiar convergence of
different quantities ('masses', related to the ) to the unique mass gap
of the nonlinear sigma model and analyse the first next-to-leading order
corrections.Comment: Latex version, journal version (with explanatory appendices and more
references
Generalised scaling at subleading order
We study operators in the sl(2) sector of N=4 SYM in the generalised scaling
limit, where the spin is large and the length of the operator scales with the
logarithm of the spin. At leading order in the large spin expansion the scaling
dimension at strong coupling is given in terms of the free energy of the O(6)
model. We investigate the first subleading corrections to the scaling dimension
and find that these too can be derived from the O(6) model in the strong
coupling limit.Comment: 19 pages, v2: Equation corrected and references added, v3: references
added, published versio
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