Notes on Operator Equations of Supercurrent Multiplets and the Anomaly Puzzle in Supersymmetric Field Theories

Recently, Komargodski and Seiberg have proposed a new type of supercurrent multiplet which contains the energy-momentum tensor and the supersymmetry current consistently. In this paper we study quantum properties of the supercurrent in renormalizable field theories. We point out that the new supercurrent gives a quite simple resolution to the classic problem, called the anomaly puzzle, that the Adler-Bardeen theorem applied to an R-symmetry current is inconsistent with all order corrections to $\beta$ functions. We propose an operator equation for the supercurrent in all orders of perturbation theory, and then perform several consistency checks of the equation. The operator equation we propose is consisitent with the one proposed by Shifman and Vainshtein, if we take some care in interpreting the meaning of non-conserved currents.Comment: 28 pages; v2:clarifications and references added, some minor change

Exactly Marginal Deformations and Global Symmetries

We study the problem of finding exactly marginal deformations of N=1 superconformal field theories in four dimensions. We find that the only way a marginal chiral operator can become not exactly marginal is for it to combine with a conserved current multiplet. Additionally, we find that the space of exactly marginal deformations, also called the "conformal manifold," is the quotient of the space of marginal couplings by the complexified continuous global symmetry group. This fact explains why exactly marginal deformations are ubiquitous in N=1 theories. Our method turns the problem of enumerating exactly marginal operators into a problem in group theory, and substantially extends and simplifies the previous analysis by Leigh and Strassler. We also briefly discuss how to apply our analysis to N=2 theories in three dimensions.Comment: 23 pages, 2 figure

Superconformal Flavor Simplified

A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler many supersymmetric models of this type were considered to be 'incalculable' because the R-charges were not sufficiently constrained by the superpotential. We point out that nearly all such models are calculable with the use of a-maximization. Utilizing this, we construct the simplest vector-like flavor models and discuss their viability. A significant constraint on these models comes from requiring that the visible gauge couplings remain perturbative throughout the conformal window needed to generate the hierarchies. However, we find that there is a small class of simple flavor models that can evade this bound.Comment: 43 pages, 1 figure; V3: small corrections and clarifications, references adde

Holographic Conformal Window - A Bottom Up Approach

We propose a five-dimensional framework for modeling the background geometry associated to ordinary Yang-Mills (YM) as well as to nonsupersymmetric gauge theories possessing an infrared fixed point with fermions in various representations of the underlying gauge group. The model is based on the improved holographic approach, on the string theory side, and on the conjectured all-orders beta function for the gauge theory one. We first analyze the YM gauge theory. We then investigate the effects of adding flavors and show that, in the holographic description of the conformal window, the geometry becomes AdS when approaching the ultraviolet and the infrared regimes. As the number of flavors increases within the conformal window we observe that the geometry becomes more and more of AdS type over the entire energy range.Comment: 20 Pages, 3 Figures. v2: references adde

Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop

We calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory to one-loop order. In order to carry out the calculations we project the indices of the spin j operator to the light-cone and evaluate the correlator in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The results of our direct calculation are in agreement with the structure constants obtained by F.A. Dolan and H. Osborn from the operator product expansion of four-point functions of half-BPS operators.Comment: references update

A Lagrangian Approach to the Simulation of a Constricted Vacuum Arc in a Magnetic Field

The use of numerical simulations of vacuum arcs can be very useful in order to improve the performance of vacuum interrupters. Standard computational fluid dynamics methods based on the Eulerian approach have difficulties to deal with this kind of problem, so a new technique is proposed, based on a Lagrangian approach. In order to focus on the performance of the new approach and not on specific details of a full model, a simplified arc model is used to investigate the capabilities of a Lagrangian approach in the context of vacuum arc simulations. The focus of this initial study is on implementing the necessary ingredients, that is, the development of a compressible flow solver, the introduction of the relevant boundary conditions and the coupling with the current conservation equation for the electric current. In addition, the stability of such a numerical scheme is evaluated. Furthermore, comparisons with results obtained using commercial software are also provided to demonstrate the validity of the results obtained with the new methodology

A Multilevel Method for Discontinuous Galerkin Approximation of Three-dimensional Elliptic Problems

Summary. We construct optimal order multilevel preconditioners for interiorpenalty discontinuous Galerkin (DG) finite element discretizations of 3D elliptic boundary-value problems. A specific assembling process is proposed which allows us to characterize the hierarchical splitting locally. This is also the key for a local analysis of the angle between the resulting subspaces. Applying the corresponding two-level basis transformation recursively, a sequence of algebraic problems is generated. These discrete problems can be associated with coarse versions of DG approximations (of the solution to the original variational problem) on a hierarchy of geometrically nested meshes. The presented numerical results demonstrate the potential of this approach.