Revisiting instanton corrections to the Konishi multiplet

We revisit the calculation of instanton effects in correlation functions in ${\cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators do not receive instanton corrections in the semiclassical approximation. We go beyond this approximation and demonstrate that, while operators belonging to the same ${\cal N}=4$ supermultiplet ought to have the same conformal data, the evaluation of quantum instanton corrections for one operator can be mapped into a semiclassical computation for another operator in the same supermultiplet. This observation allows us to compute explicitly the leading instanton correction to the scaling dimension of operators in the Konishi supermultiplet as well as to their structure constants in the OPE of two half-BPS scalar operators. We then use these results, together with crossing symmetry, to determine instanton corrections to scaling dimensions of twist-four operators with large spin.Comment: 25 pages; v2: minor changes, typos correcte

Operator mixing in N=4 SYM: The Konishi anomaly revisited

In the context of the superconformal N=4 SYM theory the Konishi anomaly can be viewed as the descendant $K_{10}$ of the Konishi multiplet in the 10 of SU(4), carrying the anomalous dimension of the multiplet. Another descendant $O_{10}$ with the same quantum numbers, but this time without anomalous dimension, is obtained from the protected half-BPS operator $O_{20'}$ (the stress-tensor multiplet). Both $K_{10}$ and $O_{10}$ are renormalized mixtures of the same two bare operators, one trilinear (coming from the superpotential), the other bilinear (the so-called "quantum Konishi anomaly"). Only the operator $K_{10}$ is allowed to appear in the right-hand side of the Konishi anomaly equation, the protected one $O_{10}$ does not match the conformal properties of the left-hand side. Thus, in a superconformal renormalization scheme the separation into "classical" and "quantum" anomaly terms is not possible, and the question whether the Konishi anomaly is one-loop exact is out of context. The same treatment applies to the operators of the BMN family, for which no analogy with the traditional axial anomaly exists. We illustrate our abstract analysis of this mixing problem by an explicit calculation of the mixing matrix at level g^4 ("two loops") in the supersymmetric dimensional reduction scheme.Comment: 28 pp LaTeX, 3 figure

SL(2,Z) Multiplets in N=4 SYM Theory

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as part of a finite or infinite dimensional multiplet under the SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the non-perturbative local operators dual to the Konishi multiplet.Comment: 14 pages, harvmac; v2: published version with minor change

Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.Comment: 19 pages, two figures, latex. v2: reference added, small corrections. v3: corrected unbounded spectrum erro

Optimal Diversity in Investments with Recombinant Innovation

The notion of dynamic, endogenous diversity and its role in theories of investment and technological innovation is addressed. We develop a formal model of an innovation arising from the combination of two existing modules with the objective to optimize the net benefits of diversity. The model takes into account increasing returns to scale and the effect of different dimensions of diversity on the probability of emergence of a third option. We obtain analytical solutions describing the dynamic behaviour of the values of the options. Next diversity is optimized by trading off the benefits of recombinant innovation and returns to scale. We derive conditions for optimal diversity under different regimes of returns to scale. Threshold values of returns to scale and recombination probability define regions where either specialization or diversity is the best choice. In the time domain, when the investment time horizon is beyond a threshold value, a diversified investment becomes the best choice. This threshold will be larger the higher the returns to scale.

The k-junction motif in RNA structure

The k-junction is a structural motif in RNA comprising a three-way helical junction based upon kink turn (k-turn) architecture. A computer program written to examine relative helical orientation identified the three-way junction of the Arabidopsis TPP riboswitch as an elaborated k-turn. The Escherichia coli TPP riboswitch contains a related k-junction, and analysis of >11 000 sequences shows that the structure is common to these riboswitches. The k-junction exhibits all the key features of an N1-class k-turn, including the standard cross-strand hydrogen bonds. The third helix of the junction is coaxially aligned with the C (canonical) helix, while the k-turn loop forms the turn into the NC (non-canonical) helix. Analysis of ligand binding by ITC and global folding by gel electrophoresis demonstrates the importance of the k-turn nucleotides. Clearly the basic elements of k-turn structure are structurally well suited to generate a three-way helical junction, retaining all the key features and interactions of the k-turn

Body mass index and health care utilization in diabetic and nondiabetic individuals.

BackgroundAlthough controversial, most studies examining the relationship of body mass index (BMI) with mortality in diabetes suggest a paradox: the lowest risk category is above normal weight, versus normal weight in nondiabetic persons. One proposed explanation is greater morbidity of diabetes in normal weight persons. If this were so, it would suggest a health care utilization paradox in diabetes, paralleling the mortality paradox, yet no studies have examined this issue.ObjectiveTo compare the relationship of BMI with health care utilization in diabetic versus nondiabetic persons.DesignPopulation-based cross-sectional study.SubjectsAdults in the 2000-2011 Medical Expenditures Panel Surveys (N=120,389).MeasuresTotal health care expenditures, hospital utilization (≥1 admission), and emergency department utilization (≥1 visit). BMI (kg/m) categories were: <20 (underweight); 20 to <25 (normal); 25 to <30 (overweight); 30 to <35 (obese); and ≥35 (severely obese). Adjustors were age, sex, race/ethnicity, income, health insurance, education, smoking, co-morbidity, urbanicity, region, and year.ResultsAmong diabetic persons, adjusted mean total health care expenditures were significantly lower in obese versus normal weight persons ($1314, 95$513-$2115; P=0.001). By contrast, among nondiabetic persons, total expenditures were nonsignificantly higher in obese versus normal weight persons (-$229, 95% CI, -$460 to$2; P=0.052). Findings for hospital and emergency department utilization exhibited similar patterns.ConclusionsNormal weight diabetic persons used substantially more health care than their overweight and obese counterparts, a difference not observed in nondiabetic persons. These differences support the plausibility of a BMI mortality paradox related to greater morbidity of diabetes in normal weight than in heavier persons

Subleading contributions to the three-nucleon contact interaction

We obtain a minimal form of the two-derivative three-nucleon contact Lagrangian, by imposing all constraints deriving from discrete symmetries, Fierz identities and Poincare' covariance. The resulting interaction, depending on 13 unknown low-energy constants, leads to a three-nucleon potential which we give in a local form in configuration space. We also consider the leading (no-derivative) four-nucleon interaction and show that there exists only one independent operator.Comment: 11 pages. Three more operators found after correcting some mistaken Fierz relation