Plane waves from double extended spacetimes

We study exact string backgrounds (WZW models) generated by nonsemisimple algebras which are obtained as double extensions of generic D--dimensional semisimple algebras. We prove that a suitable change of coordinates always exists which reduces these backgrounds to be the product of the nontrivial background associated to the original algebra and two dimensional Minkowski. However, under suitable contraction, the algebra reduces to a Nappi--Witten algebra and the corresponding spacetime geometry, no more factorized, can be interpreted as the Penrose limit of the original background. For both configurations we construct D--brane solutions and prove that {\em all} the branes survive the Penrose limit. Therefore, the limit procedure can be used to extract informations about Nappi--Witten plane wave backgrounds in arbitrary dimensions.Comment: 27 pages, no figures, references adde

Four-point correlators of BPS operators in N=4 SYM at order g^4

We study the large N degeneracy in the structure of the four-point amplitudes of 1/2-BPS operators of arbitrary weight k in perturbative N=4 SYM theory. At one loop (order g^2) this degeneracy manifests itself in a smaller number of independent conformal invariant functions describing the amplitude, compared to AdS_5 supergravity results. To study this phenomenon at the two-loop level (order g^4) we consider a particular N=2 hypermultiplet projection of the general N=4 amplitude. Using the formalism of N=2 harmonic superspace we then explicitly compute this four-point correlator at two loops and identify the corresponding conformal invariant functions. In the cases of 1/2-BPS operators of weight k=3 and k=4 the one-loop large N degeneracy is lifted by the two-loop corrections. However, for weight k > 4 the degeneracy is still there at the two-loop level. This behavior suggests that for a given weight k the degeneracy will be removed if perturbative corrections of sufficiently high order are taken into account. These results are in accord with the AdS/CFT duality conjecture.Comment: 45 pages, latex, 14 figure

On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice

We consider a one-dimensional discrete nonlinear Schr\uf6dinger (dNLS) model featuring interactions beyond nearest neighbors. We are interested in the existence (or nonexistence) of phase-shift discrete solitons, which correspond to four-sites vortex solutions in the standard two-dimensional dNLS model (square lattice), of which this is a simpler variant. Due to the specific choice of lengths of the inter-site interactions, the vortex configurations considered present a degeneracy which causes the standard continuation techniques to be non-applicable. In the present one-dimensional case, the existence of a conserved quantity for the soliton profile (the so-called density current), together with a perturbative construction, leads to the nonexistence of any phase-shift discrete soliton which is at least C2 with respect to the small coupling \u3f5, in the limit of vanishing \u3f5. If we assume the solution to be only C0 in the same limit of \u3f5, nonexistence is instead proved by studying the bifurcation equation of a Lyapunov-Schmidt reduction, expanded to suitably high orders. Specifically, we produce a nonexistence criterion whose efficiency we reveal in the cases of partial and full degeneracy of approximate solutions obtained via a leading order expansion

Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA

We study a class of non-protected local composite operators which occur in the R symmetry singlet channel of the OPE of two stress-tensor multiplets in {\cal N}=4 SYM. At tree level these are quadrilinear scalar dimension four operators, two single-traces and two double-traces. In the presence of interaction, due to a non-trivial mixing under renormalization, they split into linear combinations of conformally covariant operators. We resolve the mixing by computing the one-loop two-point functions of all the operators in an {\cal N}=1 setup, then diagonalizing the anomalous dimension matrix and identifying the quasiprimary operators. We find one operator whose anomalous dimension is negative and suppressed by a factor of 1/N^2 with respect to the anomalous dimensions of the Konishi-like operators. We reveal the mechanism responsible for this suppression and argue that it works at every order in perturbation theory. In the context of the AdS/CFT correspondence such an operator should be dual to a multiparticle supergravity state whose energy is less than the sum of the corresponding individual single-particle states.Comment: Latex, 32 pages, 5 figure

Deformed PP-waves from the Lunin-Maldacena Background

In this article we study a pp-wave limit of the Lunin-Maldacena background. We show that the relevant string theory background is a homogeneous pp-wave. We obtain the string spectrum. The dual field theory is a deformation of N=4 super Yang-Mills theory. We have shown that, for a class of operators, at O(g_{YM}^2) and at leading order in N, all contributions to the anomalous dimension come from F-terms. We are able to identify the operator in the deformed super Yang-Mills which is dual to the lowest string mode. By studying the undeformed theory we are able to provide some evidence, directly in the field theory, that a small set of nearly protected operators decouple. We make some comments on operators in the Yang-Mills theory that are dual to excited string modes.Comment: 22 pages, 1 figure; Final version to appear in JHE

Exceptional non-renormalization properties and OPE analysis of chiral four-point functions in N=4 SYM_4

We show that certain classes of apparently unprotected operators in N=4 SYM_4 do not receive quantum corrections as a consequence of a partial non-renormalization theorem for the 4-point function of chiral primary operators. We develop techniques yielding the asymptotic expansion of the 4-point function of CPOs up to order O(\lambda^2) and we perform a detailed OPE analysis. Our results reveal the existence of new non-renormalized operators of approximate dimension 6.Comment: an error in Sect. 4 corrected; references adde

Impact of Increasing Nitrogen Fertilizer Rates upon an Irrigated Tanzania Grass Pasture. 1. Dry Matter Yield

An experiment was carried out with irrigated Tanzania grass (Panicum maximum, Jacq.) pasture receiving five nitrogen (N) rates of (0, 30, 60, 90 and 120 kg N ha-¹ cut-¹) during the growing season. N application increased dry matter yield and Tanzania growth rate linearly (P \u3c 0.05). Responses to nitrogen applications were higher in the first two cuts of the growing season than in the last two cuts. The N fertilizer conversion into herbage dry matter was also higher in the beginning of the growing season

Three-Point Functions of Quarter BPS Operators in N=4 SYM

In a recent paper hep-th/0109064, quarter-BPS chiral primaries were constructed in the fully interacting four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These operators are annihilated by four supercharges, and at order g^2 have protected scaling dimension and normalization. Here, we compute three-point functions involving these quarter-BPS operators along with half-BPS operators. The combinatorics of the problem is rather involved, and we consider the following special cases: (1) correlators of two half-BPS primaries with an arbitrary chiral primary; (2) certain classes of and < quarter quarter quarter > three-point functions; (3) three-point functions involving the Delta correlators with the special quarter-BPS operator made of single and double trace operators only. The analysis in cases (1)-(3) is valid for general N, while (4) is a large N approximation. Order g^2 corrections to all three-point functions considered in this paper are found to vanish. In the AdS/CFT correspondence, quarter-BPS chiral primaries are dual to threshold bound states of elementary supergravity excitations. We present a supergravity discussion of two- and three-point correlators involving these bound states.Comment: 44 pages, Latex, eps figures, uses epsfig.sty; references adde