66,954 research outputs found
Generic Traces and Constraints, GenTra4CP revisited
The generic trace format GenTra4CP has been defined in 2004 with the goal of
becoming a standard trace format for the observation of constraint solvers over
finite domains. It has not been used since. This paper defines the concept of
generic trace formally, based on simple transformations of traces. It then
analyzes, and occasionally corrects, shortcomings of the proposed initial
format and shows the interest that a generic tracer may bring to develop
portable applications or to standardization efforts, in particular in the field
of constraints
From counting to construction of BPS states in N=4 SYM
We describe a universal element in the group algebra of symmetric groups,
whose characters provides the counting of quarter and eighth BPS states at weak
coupling in N=4 SYM, refined according to representations of the global
symmetry group. A related projector acting on the Hilbert space of the free
theory is used to construct the matrix of two-point functions of the states
annihilated by the one-loop dilatation operator, at finite N or in the large N
limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of
symmetric groups and dimensions of U(N) representations. It is expected, by
non-renormalization theorems, to contain observables at strong coupling. Using
the stringy exclusion principle, we interpret a class of its eigenvalues and
eigenvectors in terms of giant gravitons. We also give a formula for the action
of the one-loop dilatation operator on the orthogonal basis of the free theory,
which is manifestly covariant under the global symmetry.Comment: 41 pages + Appendices, 4 figures; v2 - refs and acknowledgments adde
Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory
We continue the investigation of massive integrable models by means of the
bootstrap fusion procedure, started in our previous work on O(3) nonlinear
sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear
sigma model we prove a similar relation between sine-Gordon theory and a
one-parameter deformation of the O(3) sigma model, the sausage model. This
allows us to write down a free field representation for the
Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral
representation for the generating functions of form-factors in this theory. We
also clear up the origin of the singularities in the bootstrap construction and
the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted
for publication in Physical Review
On traces of tensor representations of diagrams
Let be a set, of {\em types}, and let \iota,o:T\to\oZ_+. A {\em
-diagram} is a locally ordered directed graph equipped with a function
such that each vertex of has indegree
and outdegree . (A directed graph is {\em locally ordered} if at
each vertex , linear orders of the edges entering and of the edges
leaving are specified.)
Let be a finite-dimensional \oF-linear space, where \oF is an
algebraically closed field of characteristic 0. A function on assigning
to each a tensor is called a {\em tensor representation} of . The {\em trace} (or {\em
partition function}) of is the \oF-valued function on the
collection of -diagrams obtained by `decorating' each vertex of a
-diagram with the tensor , and contracting tensors along
each edge of , while respecting the order of the edges entering and
leaving . In this way we obtain a {\em tensor network}.
We characterize which functions on -diagrams are traces, and show that
each trace comes from a unique `strongly nondegenerate' tensor representation.
The theorem applies to virtual knot diagrams, chord diagrams, and group
representations
Compactification of M(atrix) theory on noncommutative toroidal orbifolds
It was shown by A. Connes, M. Douglas and A. Schwarz that noncommutative tori
arise naturally in consideration of toroidal compactifications of M(atrix)
theory. A similar analysis of toroidal Z_{2} orbifolds leads to the algebra
B_{\theta} that can be defined as a crossed product of noncommutative torus and
the group Z_{2}. Our paper is devoted to the study of projective modules over
B_{\theta} (Z_{2}-equivariant projective modules over a noncommutative torus).
We analyze the Morita equivalence (duality) for B_{\theta} algebras working out
the two-dimensional case in detail.Comment: 19 pages, Latex; v2: comments clarifying the duality group structure
added, section 5 extended, minor improvements all over the tex
Explicit generating functional for pions and virtual photons
We construct the explicit one-loop functional of chiral perturbation theory
for two light flavours, including virtual photons. We stick to contributions
where 1 or 2 mesons and at most one photon are running in the loops. With the
explicit functional at hand, the evaluation of the relevant Green functions
boils down to performing traces over the flavour matrices. For illustration, we
work out the pi+ pi- -> pi0 pi0 scattering amplitude at threshold at order p^4,
e^2p^2.Comment: 20 pages, 2 figures; version accepted for publication, minor
typographical changes, acknowledgments adde
Finite-Temperature Form Factors: a Review
We review the concept of finite-temperature form factor that was introduced
recently by the author in the context of the Majorana theory.
Finite-temperature form factors can be used to obtain spectral decompositions
of finite-temperature correlation functions in a way that mimics the
form-factor expansion of the zero temperature case. We develop the concept in
the general factorised scattering set-up of integrable quantum field theory,
list certain expected properties and present the full construction in the case
of the massive Majorana theory, including how it can be applied to the
calculation of correlation functions in the quantum Ising model. In particular,
we include the ''twisted construction'', which was not developed before and
which is essential for the application to the quantum Ising model.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
A Comparison of Two Shallow Water Models with Non-Conforming Adaptive Grids: classical tests
In an effort to study the applicability of adaptive mesh refinement (AMR)
techniques to atmospheric models an interpolation-based spectral element
shallow water model on a cubed-sphere grid is compared to a block-structured
finite volume method in latitude-longitude geometry. Both models utilize a
non-conforming adaptation approach which doubles the resolution at fine-coarse
mesh interfaces. The underlying AMR libraries are quad-tree based and ensure
that neighboring regions can only differ by one refinement level.
The models are compared via selected test cases from a standard test suite
for the shallow water equations. They include the advection of a cosine bell, a
steady-state geostrophic flow, a flow over an idealized mountain and a
Rossby-Haurwitz wave. Both static and dynamics adaptations are evaluated which
reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR
simulations show that both models successfully place static and dynamic
adaptations in local regions without requiring a fine grid in the global
domain. The adaptive grids reliably track features of interests without visible
distortions or noise at mesh interfaces. Simple threshold adaptation criteria
for the geopotential height and the relative vorticity are assessed.Comment: 25 pages, 11 figures, preprin
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