6,004 research outputs found
Cutting the cylinder into squares: The square form factor
In this article we present a method for constructing two-point functions in
the spirit of the hexagon proposal, which leads us to propose a "square form
factor". Since cutting the square gives us two squares, we can write a
consistency condition that heavily constrains such form factors. In particular,
we are able to use this constraint to reconstruct the Gaudin through the forest
expansion of the determinant appearing in its definition. We also use this
procedure to compute the norm of off-shell Bethe states for some simple cases.Comment: 34 pages, 10 figure
Holographic correlation functions of hexagon Wilson loops with one local operator
We consider the ratio of the correlation function of an hexagon light-like
Wilson loop with one local operator over the expectation value of the Wilson
loop within the strong-coupling regime of the AdS/CFT correspondence. We choose
the hexagon Wilson loop within a class of minimal solutions obtained by cutting
and gluing light-like quadrangle loops. These surfaces do not have an
interpretation in terms of dual scattering amplitudes but they still exhibit
general features of the mixed correlation function. In the case of a regular
null hexagon conformal symmetry constrains the space-time dependence of the
correlator up to a function of three conformal cross-ratios. We obtain the
leading-order contribution to the correlation function in the semiclassical
approximation of large string tension, and express the result in terms of three
conformal ratios in the case where the local operator is taken to be the
dilaton. We include the analysis of an irregular Wilson loop obtained after a
boost of the regular hexagon.Comment: 12 pages. Latex. v2: Reference added. v3: Added clarifications,
published versio
Spinning strings in the -deformed Neumann-Rosochatius system
The sigma-model of closed strings spinning in the -deformation of
leads to an integrable deformation of the
one-dimensional Neumann-Rosochatius mechanical system. In this article we
construct general solutions to this system that can be written in terms of
elliptic functions. The solutions correspond to closed strings with
non-constant radii rotating with two different angular momenta in an
-deformed three-sphere. We analyse the reduction of the elliptic
solutions for some limiting values of the deformation parameter. For the case
of solutions with constant radii we find the dependence of the classical energy
of the string on the angular momenta as an expansion in the 't Hooft coupling.Comment: 17 pages. Latex. v2: Additional references. v3: Minor changes and
updated reference
Elliptic solutions in the Neumann-Rosochatius system with mixed flux
Closed strings spinning in AdS_3 x S^3 x T^4 with mixed R-R and NS-NS
three-form fluxes are described by a deformation of the one-dimensional
Neumann-Rosochatius integrable system. In this article we find general
solutions to this system that can be expressed in terms of elliptic functions.
We consider closed strings rotating either in S^3 with two different angular
momenta or in AdS_3 with one spin. In order to find the solutions we will need
to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system
to include the contribution from the flux. In the limit of pure NS-NS flux,
where the problem can be described by a supersymmetric WZW model, we find exact
expressions for the classical energy in terms of the spin and the angular
momenta of the spinning string.Comment: 18 pages. Latex. v2: Extended discussions, corrected misprints and
added reference. Published versio
Spinning strings in AdS_3 x S^3 with NS-NS flux
The sigma model describing closed strings rotating in AdS_3 x S^3 is known to
reduce to the one-dimensional Neumann-Rosochatius integrable system. In this
article we show that closed spinning strings in AdS_3 x S^3 x T^4 in the
presence of NS-NS three-form flux can be described by an extension of the
Neumann-Rosochatius system. We consider closed strings rotating with one spin
in AdS_3 and two different angular momenta in S^3. For a class of solutions
with constant radii we find the dependence of the classical energy on the spin
and the angular momenta as an expansion in the square of the 't Hooft coupling
of the theory.Comment: 14 pages. Latex. v2: Equations (3.19) and (3.28) corrected and
reference added. v3: Expanded discussion on the WZW limit and additional
references. Published version. v4: Misprints correcte
One-loop quantization of rigid spinning strings in with mixed flux
We compute the one-loop correction to the classical dispersion relation of
rigid closed spinning strings with two equal angular momenta in the background supported with a mixture of R-R and NS-NS
three-form fluxes. This analysis is extended to the case of two arbitrary
angular momenta in the pure NS-NS limit. We perform this computation by means
of two different methods. The first method relies on the Euler-Lagrange
equations for the quadratic fluctuations around the classical solution, while
the second one exploits the underlying integrability of the problem through the
finite-gap equations. We find that the one-loop correction vanishes in the pure
NS-NS limit.Comment: 35 pages. v2: Minor changes and references updated. v3: Published
versio
Bayesian non-linear matching of pairwise microarray gene expressions
In this paper, we present a Bayesian non-linear model to analyze matching pairs of
microarray expression data. This model generalizes, in terms of neural networks,
standard linear matching models. As a practical application, we analyze data of patients
with Acute Lymphoblastic Leukemia and we find out the best neural net model that
relates the expression levels of two types of cytogenetically different samples from
them
Spatial matching of M configurations of points with a bioinformatics application
In this paper, we present a model to deal with the problem of matching M objects or configurations of
points. This is a generalization of the model proposed by Green and Mardia (2006). We consider, as a
direct and simple application, the case of three configurations with labelled and with unlabelled points. In
both cases, we consider data from a microarray experiment of gorilla, bonobo and human cultured
fibroblasts published by Karaman et al. (2003). We find out the matchings and the best affine
transformation between the projections of genes in a two dimensional space, obtained by a
Multidimensional Scaling technique
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