70 research outputs found
On the finite size corrections of anti-ferromagnetic anomalous dimensions in SYM
Non-linear integral equations derived from Bethe Ansatz are used to evaluate
finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and
immediately lower anomalous dimensions of scalar operators in SYM.
In specific, multi-loop corrections are computed in the SU(2) operator
subspace, whereas in the general SO(6) case only one loop calculations have
been finalised. In these cases, the leading finite size corrections are given
by means of explicit formul\ae and compared with the exact numerical
evaluation. In addition, the method here proposed is quite general and
especially suitable for numerical evaluations.Comment: 38 pages, Latex revised version: draft formulae indicator deleted,
one reference added, typos corrected, few minor text modification
Integrals of motion from TBA and lattice-conformal dictionary
The integrals of motion of the tricritical Ising model are obtained by
Thermodynamic Bethe Ansatz (TBA) equations derived from the A_4 integrable
lattice model. They are compared with those given by the conformal field theory
leading to a unique one-to-one lattice-conformal correspondence. They can also
be followed along the renormalization group flows generated by the action of
the boundary field \phi_{1,3} on conformal boundary conditions in close analogy
to the usual TBA description of energies.Comment: 20 pages, 1 figure, LaTeX; v2: added references, improved conventions
introduced in sections 4, 5 and related tables; v3: added reference
A Renormalisation group for TCSA
We discuss the errors introduced by level truncation in the study of boundary
renormalisation group flows by the Truncated Conformal Space Approach. We show
that the TCSA results can have the qualitative form of a sequence of RG flows
between different conformal boundary conditions. In the case of a perturbation
by the field phi(13), we propose a renormalisation group equation for the
coupling constant which predicts a fixed point at a finite value of the TCSA
coupling constant and we compare the predictions with data obtained using TBA
equations.Comment: 11 pages, 7 figures, talk presented by G Watts at the workshop
"Integrable Models and Applications: from Strings to Condensed Matter",
Santiago de Compostela, Spain, 12-16 September 200
An evolutionary model with Turing machines
The development of a large non-coding fraction in eukaryotic DNA and the
phenomenon of the code-bloat in the field of evolutionary computations show a
striking similarity. This seems to suggest that (in the presence of mechanisms
of code growth) the evolution of a complex code can't be attained without
maintaining a large inactive fraction. To test this hypothesis we performed
computer simulations of an evolutionary toy model for Turing machines, studying
the relations among fitness and coding/non-coding ratio while varying mutation
and code growth rates. The results suggest that, in our model, having a large
reservoir of non-coding states constitutes a great (long term) evolutionary
advantage.Comment: 16 pages, 7 figure
Generalised integrable Hubbard models
We construct the XX and Hubbard-like models based on unitary superalgebras
gl(N|M) generalizing Shastry's and Maassarani's approach. We introduce the
R-matrix of the gl(N|M) XX-type model; the one of the Hubbard-like model is
defined by "coupling" two independent XX models. In both cases, we show that
the R-matrices satisfy the Yang-Baxter equation. We derive the corresponding
local Hamiltonian in the transfer matrix formalism and we determine its
symmetries. A perturbative calculation "\`a la Klein and Seitz" is performed.
Some explicit examples are worked out. We give a description of the
two-particle scattering.Comment: Talk given by G. Feverati at the workshop "RAQIS'07 Recent Advances
in Quantum Integrable Systems", 11-14 Sept. 2007, LAPTH, Annecy-le-Vieux,
Franc
Physical Combinatorics and Quasiparticles
We consider the physical combinatorics of critical lattice models and their
associated conformal field theories arising in the continuum scaling limit. As
examples, we consider A-type unitary minimal models and the level-1 sl(2)
Wess-Zumino-Witten (WZW) model. The Hamiltonian of the WZW model is the
invariant XXX spin chain. For simplicity, we consider these
theories only in their vacuum sectors on the strip. Combinatorially, fermionic
particles are introduced as certain features of RSOS paths. They are composites
of dual-particles and exhibit the properties of quasiparticles. The particles
and dual-particles are identified, through an energy preserving bijection, with
patterns of zeros of the eigenvalues of the fused transfer matrices in their
analyticity strips. The associated (m,n) systems arise as geometric packing
constraints on the particles. The analyticity encoded in the patterns of zeros
is the key to the analytic calculation of the excitation energies through the
Thermodynamic Bethe Ansatz (TBA). As a by-product of our study, in the case of
the WZW or XXX model, we find a relation between the location of the Bethe root
strings and the location of the transfer matrix 2-strings.Comment: 57 pages, in version 2: typos corrected, some sentences clarified,
one appendix remove
Hubbard's Adventures in SYM-land? Some non-perturbative considerations on finite length operators
As the Hubbard energy at half filling is believed to reproduce at strong
coupling (part of) the all loop expansion of the dimensions in the SU(2) sector
of the planar SYM, we compute an exact non-perturbative
expression for it. For this aim, we use the effective and well-known idea in 2D
statistical field theory to convert the Bethe Ansatz equations into two coupled
non-linear integral equations (NLIEs). We focus our attention on the highest
anomalous dimension for fixed bare dimension or length, , analysing the many
advantages of this method for extracting exact behaviours varying the length
and the 't Hooft coupling, . For instance, we will show that the large
(asymptotic) expansion is exactly reproduced by its analogue in the BDS
Bethe Ansatz, though the exact expression clearly differs from the BDS one (by
non-analytic terms). Performing the limits on and in different
orders is also under strict control. Eventually, the precision of numerical
integration of the NLIEs is as much impressive as in other easier-looking
theories.Comment: On the 75-th Anniversary of Bethe Ansatz, 37 Pages, Latex fil
Critical RSOS and Minimal Models II: Building Representations of the Virasoro Algebra and Fields
We consider sl(2) minimal conformal field theories and the dual parafermion
models. Guided by results for the critical A_L Restricted Solid-on-Solid (RSOS)
models and its Virasoro modules expressed in terms of paths, we propose a
general level-by-level algorithm to build matrix representations of the
Virasoro generators and chiral vertex operators (CVOs). We implement our scheme
for the critical Ising, tricritical Ising, 3-state Potts and Yang-Lee theories
on a cylinder and confirm that it is consistent with the known two-point
functions for the CVOs and energy-momentum tensor. Our algorithm employs a
distinguished basis which we call the L_1-basis. We relate the states of this
canonical basis level-by-level to orthonormalized Virasoro states
- …