Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page

Parametric evaluation of ball milling of SiC in water

A statistically designed experiment was conducted to determine optimum conditions for ball milling alpha-SiC in water. The influence of pH adjustment, volume percent solids loading, and mill rotational speed on grinding effectiveness was examined. An equation defining the effect of those milling variables on specific surface area was obtained. The volume percent solids loading of the slurry had the greatest influence on the grinding effectiveness in terms of increase in specific surface area. As grinding effectiveness improved, mill and media wear also increased. Contamination was minimized by use of sintered alpha-SiC milling hardware

Particle size reduction of Si3N4 with Si3N4 milling hardware

The grinding of Si3N4 powder using reaction bonded Si3N4 attrition, vibratory, and ball mills with Si3N4 media was examined. The rate of particle size reduction and the change in the chemical composition of the powder were determined in order to compare the grinding efficiency and the increase in impurity content resulting from mill and media wear for each technique. Attrition and vibratory milling exhibited rates of specific surface area increase that were approximately eight times that observed in ball milling. Vibratory milling introduced the greatest impurity pickup

The dual of Janus -:- an interface CFT

We propose and study a specific gauge theory dual of the smooth, non-supersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in hep-th/0304129. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary Tr(X^I X^J) and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g^2_{YM}, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value are protected to all orders in g^2_{YM}N, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. SO(3,2) symmetry requires vanishing vacuum energy, =0, and this is confirmed in first order in the discontinuity.Comment: 24 pages, 1 figure; references adde

Holographic RG-flows and Boundary CFTs

Solutions of $(d+1)$-dimensional gravity coupled to a scalar field are obtained, which holographically realize interface and boundary CFTs. The solution utilizes a Janus-like $\mathrm{AdS}_d$ slicing ansatz and corresponds to a deformation of the CFT by a spatially-dependent coupling of a relevant operator. The BCFT solutions are singular in the bulk, but physical quantities such as the holographic entanglement entropy can be calculated.Comment: 26 pages, 11 figure

From Soft Walls to Infrared Branes

Five dimensional warped spaces with soft walls are generalizations of the standard Randall-Sundrum compactifications, where instead of an infrared brane one has a curvature singularity (with vanishing warp factor) at finite proper distance in the bulk. We project the physics near the singularity onto a hypersurface located a small distance away from it in the bulk. This results in a completely equivalent description of the soft wall in terms of an effective infrared brane, hiding any singular point. We perform explicitly this calculation for two classes of soft wall backgrounds used in the literature. The procedure has several advantages. It separates in a clean way the physics of the soft wall from the physics of the five dimensional bulk, facilitating a more direct comparison with standard two-brane warped compactifications. Moreover, consistent soft walls show a sort of universal behavior near the singularity which is reflected in the effective brane Lagrangian. Thirdly, for many purposes, a good approximation is obtained by assuming the bulk background away from the singularity to be the usual Randall-Sundrum metric, thus making the soft wall backgrounds better analytically tractable. We check the validity of this procedure by calculating the spectrum of bulk fields and comparing it to the exact result, finding very good agreement.Comment: 14 pages, 2 figures, v2: subsection on IR brane potentials and appendix on fermions added, version to appear in PR

Supersymmetry algebra in N = 1 chiral supergravity

We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian for $N = 1$ supergravity (SUGRA) with the complex tetrad following the method used in the usual $N = 1$ SUGRA, and present the explicit form of the SUSY trasformations in the first-order form. The SUSY transformations are generated by two independent Majorana spinor parameters, which are apparently different from the constrained parameters employed in the method of the 2-form gravity. We also calculate the commutator algebra of the SUSY transformations on-shell.Comment: 10 pages, late