Konishi anomaly approach to gravitational F-terms

We study gravitational corrections to the effective superpotential in theories with a single adjoint chiral multiplet, using the generalized Konishi anomaly and the gravitationally deformed chiral ring. We show that the genus one correction to the loop equation in the corresponding matrix model agrees with the gravitational corrected anomaly equations in the gauge theory. An important ingrediant in the proof is the lack of factorization of chiral gauge invariant operators in presence of a supergravity background. We also find a genus zero gravitational correction to the superpotential, which can be removed by a field redefinition.Comment: 28 pages, uses JHEP3.cl

Chiral rings, anomalies and loop equations in N=1* gauge theories

We examine the equivalence between the Konishi anomaly equations and the matrix model loop equations in N=1* gauge theories, the mass deformation of N=4 supersymmetric Yang-Mills. We perform the superfunctional integral of two adjoint chiral superfields to obtain an effective N=1 theory of the third adjoint chiral superfield. By choosing an appropriate holomorphic variation, the Konishi anomaly equations correctly reproduce the loop equations in the corresponding three-matrix model. We write down the field theory loop equations explicitly by using a noncommutative product of resolvents peculiar to N=1* theories. The field theory resolvents are identified with those in the matrix model in the same manner as for the generic N=1 gauge theories. We cover all the classical gauge groups. In SO/Sp cases, both the one-loop holomorphic potential and the Konishi anomaly term involve twisting of index loops to change a one-loop oriented diagram to an unoriented diagram. The field theory loop equations for these cases show certain inhomogeneous terms suggesting the matrix model loop equations for the RP2 resolvent.Comment: 23 pages, 3 figures, latex2e, v4: minor changes in introduction and conclusions, 4 references are added, version to appear in JHE

Clarifying Some Remaining Questions in the Anomaly Puzzle

We discuss several points that may help to clarify some questions that remain about the anomaly puzzle in supersymmetric theories. In particular, we consider a general N=1 supersymmetric Yang-Mills theory. The anomaly puzzle concerns the question of whether there is a consistent way to put the R-current and the stress tensor in a single supercurrent, even though in the classical theory they are in the same supermultiplet. As is well known, the classically conserved supercurrent bifurcates into two supercurrents having different anomalies in the quantum regime. The most interesting result we obtain is an explicit expression for the lowest component of one of the two supercurrents in 4-dimensional spacetime, namely the supercurrent that has the energy-momentum tensor as one of its components. This expression for the lowest component is an energy-dependent linear combination of two chiral currents, which itself does not correspond to a classically conserved chiral current. The lowest component of the other supercurrent, namely, the R-current, satisfies the Adler-Bardeen theorem. The lowest component of the first supercurrent has an anomaly that we show is consistent with the anomaly of the trace of the energy-momentum tensor. Therefore, we conclude that there is no consistent way to put the R-current and the stress tensor in a single supercurrent in the quantized theory. We also discuss and try to clarify some technical points in the derivations of the two-supercurrents in the literature. These latter points concern the significance of infrared contributions to the NSVZ beta-function and the role of the equations of motion in deriving the two supercurrents.Comment: 22 pages, no figure. v2: minor changes. v3: sections re-organized. new subsections (IVA, IVB) added. references adde

On the Background Field Method Beyond One Loop: A manifestly covariant derivative expansion in super Yang-Mills theories

There are currently many string inspired conjectures about the structure of the low-energy effective action for super Yang-Mills theories which require explicit multi-loop calculations. In this paper, we develop a manifestly covariant derivative expansion of superspace heat kernels and present a scheme to evaluate multi-loop contributions to the effective action in the framework of the background field method. The crucial ingredient of the construction is a detailed analysis of the properties of the parallel displacement propagators associated with Yang-Mills supermultiples in N-extended superspace.Comment: 32 pages, latex, 7 EPS figures. v2: references, comments added, typos corrected, incorrect `skeleton' conjecture in sect. 3 replaced by a more careful treatment. v3: typos corrected, final version published in JHE

On the perturbative chiral ring for marginally deformed N=4 SYM theories

For \cal{N}=1 SU(N) SYM theories obtained as marginal deformations of the \cal{N}=4 parent theory we study perturbatively some sectors of the chiral ring in the weak coupling regime and for finite N. By exploiting the relation between the definition of chiral ring and the effective superpotential we develop a procedure which allows us to easily determine protected chiral operators up to n loops once the superpotential has been computed up to (n-1) order. In particular, for the Lunin-Maldacena beta-deformed theory we determine the quantum structure of a large class of operators up to three loops. We extend our procedure to more general Leigh-Strassler deformations whose chiral ring is not fully understood yet and determine the weight-two and weight-three sectors up to two loops. We use our results to infer general properties of the chiral ring.Comment: LaTex, 40 pages, 4 figures, uses JHEP3; v2: minor correction

D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace

The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant of the non(anti)commutativity parameter $C^{\alpha\beta}$. The theory is explicitly shown to preserve half of the N=2 supersymmetry, to all orders in (det C)^n. The results are further generalized to include arbitrary superpotentials as well.Comment: 32 pages, Latex; v2:minor typos corrected and a reference adde

Recreational Physical Activity and Risk of Incident Knee Osteoarthritis: An International Meta-Analysis of Individual Participant–Level Data

Objective: The effect of physical activity on the risk of developing knee osteoarthritis (OA) is unclear. We undertook this study to examine the relationship between recreational physical activity and incident knee OA outcomes using comparable physical activity and OA definitions. Methods: Data were acquired from 6 global, community-based cohorts of participants with and those without knee OA. Eligible participants had no evidence of knee OA or rheumatoid arthritis at baseline. Participants were followed up for 5–12 years for incident outcomes including the following: 1) radiographic knee OA (Kellgren-Lawrence [K/L] grade ≥2), 2) painful radiographic knee OA (radiographic OA with knee pain), and 3) OA-related knee pain. Self-reported recreational physical activity included sports and walking/cycling activities and was quantified at baseline as metabolic equivalents of task (METs) in days per week. Risk ratios (RRs) were calculated and pooled using individual participant data meta-analysis. Secondary analysis assessed the association between physical activity, defined as time (hours per week) spent in recreational physical activity and incident knee OA outcomes. Results: Based on a total of 5,065 participants, pooled RR estimates for the association of MET days per week with painful radiographic OA (RR 1.02 [95% confidence interval (95% CI) 0.93–1.12]), radiographic OA (RR 1.00 [95% CI 0.94–1.07]), and OA-related knee pain (RR 1.00 [95% CI 0.96–1.04]) were not significant. Similarly, the analysis of hours per week spent in physical activity also showed no significant associations with all outcomes. Conclusion: Our findings suggest that whole-body, physiologic energy expenditure during recreational activities and time spent in physical activity were not associated with incident knee OA outcomes

Search for heavy long-lived charged R-hadrons with the ATLAS detector in 3.2 fb(-1) of proton-proton collision data at root s=13 TeV

A search for heavy long-lived charged R-hadrons is reported using a data sample corresponding to 3.2 fb−1 of proton–proton collisions at √s = 13 TeV collected by the ATLAS experiment at the Large Hadron Collider at CERN. The search is based on observables related to large ionisation losses and slow propagation velocities, which are signatures of heavy charged particles travelling significantly slower than the speed of light. No significant deviations from the expected background are observed. Upper limits at 95% confidence level are provided on the production cross section of long-lived R-hadrons in the mass range from 600 GeV to 2000 GeV and gluino, bottom and top squark masses are excluded up to 1580 GeV, 805 GeV and 890 GeV, respectively