Calibrated Geometries and Non Perturbative Superpotentials in M-Theory

We consider non perturbative effects in M-theory compactifications on a seven-manifold of G_2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength.Comment: Latex file. 17 pages. A different decomposition for gamma matrices used. Journal versio

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

Wilson Loops in the Higgs Phase of Large N Field Theories on the Conifold

We study the quark-antiquark interaction in the large N limit of the superconformal field theory on D-3branes at a Calabi-Yau conical singularity. We compute the Wilson loop in the AdS_5xT^{11} supergravity background for the SU(2N)x SU(2N) theory. We also calculate the Wilson loop for the Higgs phase where the gauge group is broken to SU(N)x SU(N)x SU_D(N). This corresponds to a two center configuration with some of the branes at the singularity and the rest of them at a smooth point. The calculation exhibits the expected Coulomb dependence for the interaction. The angular distribution of the BPS states is different than the one for a spherical horizon.Comment: Latex2e file. 19 pages. Final versio

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

Spin chain sigma models with fermions

The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.Comment: 16 pages. Latex. v2: Misprints corrected and references adde

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.

Spinning strings in the η\eta-deformed Neumann-Rosochatius system

The sigma-model of closed strings spinning in the $\eta$-deformation of $AdS_{5} \times S^{5}$ 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 $\eta$-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

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