The magnon kinematics of the AdS/CFT correspondence

The planar dilatation operator of N=4 supersymmetric Yang-Mills is the hamiltonian of an integrable spin chain whose length is allowed to fluctuate. We will identify the dynamics of length fluctuations of planar N=4 Yang-Mills with the existence of an abelian Hopf algebra Z symmetry with non-trivial co-multiplication and antipode. The intertwiner conditions for this Hopf algebra will restrict the allowed magnon irreps to those leading to the magnon dispersion relation. We will discuss magnon kinematics and crossing symmetry on the spectrum of Z. We also consider general features of the underlying Hopf algebra with Z as central Hopf subalgebra, and discuss the giant magnon semiclassical regime.Comment: 21 pages, Latex. v2: Minor changes and additional reference

Integrability and non-perturbative effects in the AdS/CFT correspondence

We present a non-perturbative resummation of the asymptotic strong-coupling expansion for the dressing phase factor of the AdS_5xS^5 string S-matrix. The non-perturbative resummation provides a general form for the coefficients in the weak-coupling expansion, in agreement with crossing symmetry and transcendentality. The ambiguities of the non-perturbative prescription are discussed together with the similarities with the non-perturbative definition of the c=1 matrix model.Comment: 8 pages. Late

M-Theory, Torons and Confinement

We study the decompactification limit of M-theory superpotentials for N=1 four dimensional supersymmetric gauge theories. These superpotentials can be interpreted as generated by toron configurations. The connection with the confinement picture in the maximal abelian gauge is discussed.Comment: Latex file. 9 pages. Lecture given by C. G. at the XXXIII Karpacz School: "Duality, Strings and Fields". February 1997. Improved version, with a clarifying exposition on the dynamical role of torons in M-theory include

M and F-Theory Instantons, N=1 Supersymmetry and Fractional Topological Charges

We analize instanton generated superpotentials for three dimensional N=2 supersymmetric gauge theories obtained by compactifying on S^1 N=1 four dimensional theories. In the N_f=1 case, we find that the vacua in the decompactification limit is given by the singular points of the Coulomb branch of the N=2 four dimensional theory (we also consider the massive case). The decompactification limit of the superpotential for pure gauge theories without chiral matter is interpreted in terms of `t Hooft's fractional instanton amplitudes.Comment: Latex file. 11 pages. Typos corrected. Section on QCD has been rewritten, clarifying some points, and a reference has been added. Final version to appear at Int. Jour. Mod. Phys.

Child health in rural Colombia: determinants and policy interventions

In this paper we study the determinants of child anthropometrics on a sample of poor Colombian children living in small municipalities. We focus on the influence of household consumption, and public infrastructure. We take into account the endogeneity of household consumption using two different sets of instruments: household assets and municipality average wage. We find that household consumption is an important determinant of child health. The importance of the effect is confirmed by the two different sets of instruments. We find that using ordinary least squares would lead to conclude that the importance of household consumption is much smaller than the instrumental variable estimates suggest. The presence of a public hospital in the municipality positively influences child health. The extent of the piped water network positively influences the health of children if their parents have at least some education. The number of hours of growth and development check-ups is also an important determinant of child health. We find that some of these results only show up once squared and interaction terms have been included in the regression. Overall, our estimates suggest that both public and private investments are important to improve child health in poor environments

Magnons and BFKL

We extract from the double logarithmic contributions to DGLAP anomalous dimensions for twist-two operators up to three-loops the magnon dispersion relation for planar N=4 supersymmetric Yang-Mills. Perturbatively the magnon dispersion relation agrees with the expansion of the anomalous dimension for spin-one as well as with the non-collinear double logarithmic contributions to the BFKL anomalous dimensions analytically extended to negative spin. The all-loop expression for the magnon dispersion relation is determined by the double logarithmic resummation of the corresponding Bethe-Salpeter equation. A potential map relating the spin chain magnon to BFKL eigenfunctions in the double logarithm approximation is suggested.Comment: 21 pages. Latex. v2: Reference added and minor change