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

Microscopic model of diffusion limited aggregation and electrodeposition in the presence of levelling molecules

A microscopic model of the effect of unbinding in diffusion limited aggregation based on a cellular automata approach is presented. The geometry resembles electrochemical deposition - ``ions'' diffuse at random from the top of a container until encountering a cluster in contact with the bottom, to which they stick. The model exhibits dendritic (fractal) growth in the diffusion limited case. The addition of a field eliminates the fractal nature but the density remains low. The addition of molecules which unbind atoms from the aggregate transforms the deposit to a 100% dense one (in 3D). The molecules are remarkably adept at avoiding being trapped. This mimics the effect of so-called ``leveller'' molecules which are used in electrochemical deposition

Studies of discharge mechanisms in high pressure gases-applications to high efficiency high power lasers

By measuring the absorption and emission cantinua of various states in the cesium/xenon molecule, the collisional rates critical in populating the alkali/rare gas excimer levels have been estimated. Cs atomic states that are weakly optically connected to ground have been shown to form excimer levels that are attractive as potential dissociation lasers. In particular, the (Cs/7 2S/Xe) excited molecule appears promising as a source of high energy laser radiation due to its large dissociation energy, stimulated emission cross section, and small population inversion densities. Monitoring of the optically pumped Cs2 molecular absorption profile in the presence of xenon shows a drastic change with increasing xenon pressure for the Cs2C band. Dominant absorption at large xenon densities is centered around approximately 6380 A as opposed to 6300 A for lower perturber pressure

Nonlinear field theories during homogeneous spatial dilation

The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the properties of nonlinear field theories embedded in expanding Euclidean Friedmann-Lema\^{\i}tre-Robertson-Walker metrics in the context of cosmology, as well as different systems in the disciplines of statistical mechanics and condensed matter physics. Field theories are characterized by the speed at which they propagate correlations within themselves. We show that for linear field theories correlations stop propagating if and only if the speed at which the space dilates is higher than the speed at which correlations propagate. The situation is in general different for nonlinear field theories. In this case correlations might stop propagating even if the velocity at which space dilates is lower than the velocity at which correlations propagate. In particular, these results imply that it is not possible to characterize the dynamics of a nonlinear field theory during homogeneous spatial dilation {\it a priori}. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang equation

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

Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling

We construct an exact analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high spin operators in planar N=4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.Comment: 5 pages. v3: minor corrections, references and important note adde

AdS/SCFT in Superspace

A discussion of the AdS/CFT correspondence in IIB is given in a superspace context. The main emphasis is on the properties of SCFT correlators on the boundary which are studied using harmonic superspace techniques. These techniques provide the easiest way of implementing the superconformal Ward identities. The Ward identities, together with analyticity, can be used to give a compelling argument in support of the non-renormalisation theorems for two- and three-point functions, and to establish the triviality of extremal and next-to-extremal correlation functions. The OPE in is also briefly discussed.Comment: 10 pages; talk given by PSH at 2nd Gursey Memorial Conference, June 200

An Index for 4 dimensional Super Conformal Theories

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times$ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.Comment: harvmac 40+16 pages, v3: references and table of contents added, typos fixe