Superconformal transformations of theN=4 supersymmetric Yang-Mills theory

We obtain the superconformal transformation laws of theN=4 supersymmetric Yang-Mills theory and explicitly demonstrate the closure of the algebra.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Averting biodiversity collapse in tropical forest protected areas

The rapid disruption of tropical forests probably imperils global biodiversity more than any other contemporary phenomenon(1-3). With deforestation advancing quickly, protected areas are increasingly becoming final refuges for threatened species and natural ecosystem processes. However, many protected areas in the tropics are themselves vulnerable to human encroachment and other environmental stresses(4-9). As pressures mount, it is vital to know whether existing reserves can sustain their biodiversity. A critical constraint in addressing this question has been that data describing a broad array of biodiversity groups have been unavailable for a sufficiently large and representative sample of reserves. Here we present a uniquely comprehensive data set on changes over the past 20 to 30 years in 31 functional groups of species and 21 potential drivers of environmental change, for 60 protected areas stratified across the world's major tropical regions. Our analysis reveals great variation in reserve `health': about half of all reserves have been effective or performed passably, but the rest are experiencing an erosion of biodiversity that is often alarmingly widespread taxonomically and functionally. Habitat disruption, hunting and forest-product exploitation were the strongest predictors of declining reserve health. Crucially, environmental changes immediately outside reserves seemed nearly as important as those inside in determining their ecological fate, with changes inside reserves strongly mirroring those occurring around them. These findings suggest that tropical protected areas are often intimately linked ecologically to their surrounding habitats, and that a failure to stem broad-scale loss and degradation of such habitats could sharply increase the likelihood of serious biodiversity declines.

EFFECT OF OFF-STOICHIOMETRY AND TERNARY ADDITIONS ON PLANAR FAULT ENERGIES IN Ni3Al

First principles calculations were done to evaluate the lattice parameter, cohesive energy and stacking fault energies of ordered gamma' (Ll(2)) precipitates in superalloys as a function of composition. It was found that addition of Ti and Ta lead to an increase in lattice parameter and decrease in cohesive energy, while Ni antisites had the opposite effect. Ta and Ti addition to stoichiometric Ni3Al resulted in an initial increase in the energies of APB((111)), CSF(111), APB((001)) and SISF(111). However, at higher concentrations, the fault energies decreased. Addition of Ni antisites decreased the energy of all four faults monotonically. A model based on nearest neighbor bonding was used for Ni-3(Al, Ta), Ni-3(Al, Ti) and Ni-3(Al, Ni) pseudo-binary systems and extended to pseudo- ternary Ni-3(Al, Ta, Ni) and Ni-3(Al, Ti, Ni) systems. Recipes were developed for predicting lattice parameters, cohesive energies and fault energies in pseudo- ternary systems on the basis of coefficients derived from simpler pseudobinary systems. The model predictions were found to be in good agreement with first principles calculations for lattice parameters, cohesive energies, and energies of APB((111)) and CSF(111).

Structure constants of beta deformed super Yang-Mills

We study the structure constants of the N = 1 beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS(5) x S-5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.