On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills

We determine the exact vacuum structure of a marginal deformation of N=4 SUSY Yang-Mills with gauge group U(N). The Coulomb branch of the theory consists of several sub-branches which are governed by complex curves of the form Sigma_{n_{1}} U Sigma_{n_{2}} U Sigma_{n_{3}} of genus N=n_{1}+n_{2}+n_{3}. Each sub-branch intersects with a family of Higgs and Confining branches permuted by SL(2,Z) transformations. We determine the curve by solving a related matrix model in the planar limit according to the prescription of Dijkgraaf and Vafa, and also by explicit instanton calculations using a form of localization on the instanton moduli space. We find that Sigma_{n} coincides with the spectral curve of the n-body Ruijsenaars-Schneider system. Our results imply that the theory on each sub-branch is holomorphically equivalent to certain five-dimensional gauge theory with eight supercharges. This equivalence also implies the existence of novel confining branches in five dimensions.Comment: LaTeX file. 48 page

Yangians in Deformed Super Yang-Mills Theories

We discuss the integrability structure of deformed, four-dimensional N=4 super Yang-Mills theories using Yangians. We employ a recent procedure by Beisert and Roiban that generalizes the beta deformation of Lunin and Maldacena to produce N=1 superconformal gauge theories, which have the superalgebra SU(2,2|1)xU(1)xU(1). The deformed theories, including those with the more general twist, were shown to have retained their integrable structure. Here we examine the Yangian algebra of these deformed theories. In a five field subsector, we compute the two cases of SU(2)xU(1)xU(1)xU(1) and SU(2|1)xU(1)xU(1) as residual symmetries of SU(2,2|1)xU(1)xU(1). We compute a twisted coproduct for these theories, and show that only for the residual symmetry do we retain the standard coproduct. The twisted coproduct thus provides a method for symmetry breaking. However, the full Yangian structure of SU(2|3) is manifest in our subsector, albeit with twisted coproducts, and provides for the integrability of the theory.Comment: 17 page

Solving matrix models using holomorphy

We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by holomorphy. It is argued that these quantum deformations give rise to non-trivial relations for generalized resolvents that must hold in the associated matrix model. These relations allow to solve a sector of the associated matrix model in a similar way to a one-matrix model, by studying a curve that encodes the generalized resolvents. At the level of loop equations for the matrix model, the situations with a moduli space can sometimes be considered as a degeneration of an infinite set of linear equations, and the quantum moduli space encodes the consistency conditions for these equations to have a solution.Comment: 38 pages, JHEP style, 1 figur

Four-loop anomalous dimensions in Leigh-Strassler deformations

We determine the scalar part of the four-loop chiral dilatation operator for Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to find the four-loop anomalous dimensions for operators in closed scalar subsectors. This includes the SU(2) subsector of the (complex) beta-deformation, where we explicitly compute the anomalous dimension for operators with a single impurity. It also includes the "3-string null" operators of the cubic Leigh-Strassler deformation. Our four-loop results show that the rational part of the anomalous dimension is consistent with a conjecture made in arXiv:1108.1583 based on the three-loop result of arXiv:1008.3351 and the N=4 magnon dispersion relation. Here we find additional zeta(3) terms.Comment: Latex, feynmp, 21 page

Supergraphs and the cubic Leigh-Strassler model

We discuss supergraphs and their relation to "chiral functions" in N=4 Super Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop result of Sieg's we make an all loop conjecture for the rational contributions of certain classes of supergraphs. We then apply superspace techniques to the "cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that there are order 2^L/L single trace operators of length L which have zero anomalous dimensions to all loop order in the planar limit. We then compute the anomalous dimensions for another class of single trace operators we call one-pair states. Using the conjecture we can find a simple expression for the rational part of the anomalous dimension which we argue is valid at least up to and including five-loop order. Based on an explicit computation we can compute the anomalous dimension for these operators to four loops.Comment: 22 pages; v2: Conjecture modified to apply only for the rational part of the chiral functions. Typos fixed. Minor modification

Nodule detection in digital chest radiography: part of image background acting as pure noise

There are several factors that influence the radiologist's ability to detect a specific structure/lesion in a radiograph. Three factors that are commonly known to be of major importance are the signal itself, the system noise and the projected anatomy. The aim of this study was to determine to what extent the image background acts as pure noise for the detection of subtle lung nodules in five different regions of the chest. A receiver operating characteristic (ROC) study with five observers was conducted on two different sets of images, clinical chest X-ray images and images with a similar power spectrum as the clinical images but with a random phase spectrum, resulting in an image background containing pure noise. Simulated designer nodules with a full-width-at-fifth-maximum of 10 mm but with varying contrasts were added to the images. As a measure of the part of the image background that acts as pure noise, the ratio between the contrast needed to obtain an area under the ROC curve of 0.80 in the clinical images to that in the random-phase images was used. The ratio ranged from 0.40 (in the lateral pulmonary regions) to 0.83 (in the hilar regions) indicating that there was a large difference between different regions regarding to what extent the image background acted as pure noise. and that in the hilar regions the image background almost completely acted as pure noise for the detection of 10 turn nodules

Structure of the string R-matrix

By requiring invariance directly under the Yangian symmetry, we rederive Beisert's quantum R-matrix, in a form that carries explicit dependence on the representation labels, the braiding factors, and the spectral parameters u_i. In this way, we demonstrate that there exist a rewriting of its entries, such that the dependence on the spectral parameters is purely of difference form. Namely, the latter enter only in the combination u_1-u_2, as indicated by the shift automorphism of the Yangian. When recasted in this fashion, the entries exhibit a cleaner structure, which allows to spot new interesting relations among them. This permits to package them into a practical tensorial expression, where the non-diagonal entries are taken care by explicit combinations of symmetry algebra generators.Comment: 9 pages, LaTeX; typos correcte

Exploring the role of Facebook in re-shaping backpacker’s social interactions

The recent Facebook launch of Timeline, Social Graph Search, and the increased use of the mobile Facebook apps has resulted in some important implications for the use of Facebook by backpackers. The purpose of this paper is to (re) explore how Facebook has impacted social relationships between backpackers and their personal, professional, and ‘fellow traveller’ networks, particularly in-light of these recent changes to Facebook and the increased reduction of anonymity while travelling. An exploratory survey was administered to 216 backpackers through social media. Descriptive analysis was conducted to explore the perceived social risks and benefits of Facebook in the context of the backpacking experience

Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba3ZnIr2O9

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba3ZnIr2O9 is a realization of a novel spin-orbital liquid state. Our results reveal that Ba3ZnIr2O9 with Ir5+ (5d(4)) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J = 0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir2O9 dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK