Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace

Certain two and three point functions of gauge invariant primary operators of ${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the $\th$-components. This allows one to read off many component descendent correlators. Our results show the only possible $g^2_{YM}$ corrections to the free field correlators are contact terms. Therefore they vanish for operators at separate points, verifying the known non-renormalization theorems. This also implies the results are consistent with ${\cal N}=4$ supersymmetry even though the Lagrangian we use has only ${\cal N}=1$ manifest supersymmetry. We repeat some of the calculations using supersymmetric Landau gauge and obtain, as expected, the same results as those of supersymmetric Feynman gauge.Comment: 10 pages, 20 eps figures, references adde

Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is reformulated as a nonautonomous recurrence in a space of time-periodic functions, where the dynamics is considered along the discrete spatial coordinate. We show that small amplitude oscillations are determined by finite-dimensional nonautonomous mappings, whose dimension depends on the solutions frequency. We consider the case of two-dimensional reduced mappings, which occurs for frequencies close to the edges of the phonon band. For an homogeneous chain, the reduced map is autonomous and reversible, and bifurcations of reversible homoclinics or heteroclinic solutions are found for appropriate parameter values. These orbits correspond respectively to discrete breathers, or dark breathers superposed on a spatially extended standing wave. Breather existence is shown in some cases for any value of the coupling constant, which generalizes an existence result obtained by MacKay and Aubry at small coupling. For an inhomogeneous chain the study of the nonautonomous reduced map is in general far more involved. For the principal part of the reduced recurrence, using the assumption of weak inhomogeneity, we show that homoclinics to 0 exist when the image of the unstable manifold under a linear transformation intersects the stable manifold. This provides a geometrical understanding of tangent bifurcations of discrete breathers. The case of a mass impurity is studied in detail, and our geometrical analysis is successfully compared with direct numerical simulations

Bright and dark breathers in Fermi-Pasta-Ulam lattices

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very well exact numerical solutions even far from the top of the phonon band. On the other hand, we study numerically large amplitude breathers non predicted in the above cited reference. In particular, for a class of asymmetric FPU potentials we find an energy threshold for the existence of exact discrete breathers, which is a relatively unexplored phenomenon in one-dimensional lattices. Bright and dark breathers superposed on a uniformly stressed static configuration are also investigated.Comment: 11 pages, 16 figure

Equilibrium Phases of Tilted Dipolar Lattice Bosons

The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid at all tilt angles $\theta$ provided that the strength of dipolar interaction is below a critical value $V_c(\theta)$. Upon increasing the interaction strength while keeping $\theta$ fixed, the superfluid phase is destabilized in favor of a checkerboard or a stripe solid depending on the tilt angle. We explore the nature of the phase transition between the two solid phases and find evidence of a micro-emulsion phase, following the Spivak-Kivelson scenario, separating these two solid phases. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the stripe solid is the most robust, making it the best candidate for experimental observation.Comment: 7 pages, 6 figure

Breathers in FPU systems, near and far from the phonon band

There exists a recent mathematical proof on the existence of small amplitude breathers in FPU systems near the phonon band, which includes a prediction of their amplitude and width. In this work we obtain numerically these breathers, and calculate the range of validity of the predictions, which extends relatively far from the phonon band. There exist also large amplitude breathers with the same frequency, with the consequence that there is an energy gap for breather creation in these systems.Comment: 3 pages, 2 figures, proceeding of the conference on Localization and to and Energy Transfer in Nonlinear Systems, June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain. To be published by World Scientifi

Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N=4 analytic superspace for $n\leq4$ points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with $n\geq 4$ points have non-trivial dependence on the Yang-Mills coupling constant.Comment: 9 page

Thermodynamics of quantum degenerate gases in optical lattices

The entropy-temperature curves are calculated for non-interacting Bose and Fermi gases in a 3D optical lattice. These curves facilitate understanding of how adiabatic changes in the lattice depth affect the temperature, and we demonstrate regimes where the atomic sample can be significantly heated or cooled by the loading process. We assess the effects of interactions on a Bose gas in a deep optical lattice, and show that interactions ultimately limit the extent of cooling that can occur during lattice loading.Comment: 6 pages, 4 figures. Submitted to proceedings of Laser Physics 2006 Worksho

The Axion and the Goldstone Higgs

We consider the renormalizable $SO(5)/SO(4)$ $\sigma$-model, in which the Higgs particle has a pseudo-Nambu-Goldstone boson character, and explore what the minimal field extension required to implement the Peccei-Quinn symmetry (PQ) is, within the partial compositeness scenario. It turns out that the minimal model does not require the enlargement of the exotic fermionic sector, but only the addition of a singlet scalar: it is sufficient that the exotic fermions involved in partial compositeness and the singlet scalar become charged under Peccei-Quinn transformations. We explore the phenomenological predictions for photonic signals in axion searches for all models discussed. Because of the constraints imposed on the exotic fermion sector by the Standard Model fermion masses, the expected range of allowed axion-photon couplings turns out to be generically narrowed with respect to that of standard invisible axion models, impacting the experimental quest.Comment: 31 pages, 2 Figures. Description improved, results unchange