Thermal Stress Tensor Correlators, OPE and Holography

In strongly coupled conformal field theories with a large central charge important light degrees of freedom are the stress tensor and its composites, multi-stress tensors. We consider the OPE expansion of two-point functions of the stress tensor in thermal and heavy states and focus on the contributions from the stress tensor and double-stress tensors in four spacetime dimensions. We compare the results to the holographic finite temperature two-point functions and read off conformal data beyond the leading order in the large central charge expansion. In particular, we compute corrections to the OPE coefficients which determine the near-lightcone behavior of the correlators. We also compute the anomalous dimensions of the double-stress tensor operators.Comment: 47 page

Volymsrapportering vid terrängtransport av virke

This report is a B.Sc. Forestry thesis work at the school for Forest Management, SLU. The work was an assignment from the forest owners’ association Mellanskog. The aim of the work where to investigate the economical result of removing undergrowth trees before first thinning, and a follow-up of the contractors and their compliance with Mellanskog standards. This thesis work was divided in three parts: The first was to find a relation between the net volume from the first thinning and the cost of cleaning undergrowth trees. Secondly there was a follow-up in the field, to investigate whether the contractors have done the undergrowth cleaning according to Mellanskog’s directives. The last part of the assignment was an inquiry examination to both thinning machine contractors and cleaning contractors, including interviews with some of them. One hypothesis, which we shared with our assigner (Mellanskog), was that all contractors didn`t follow the directives. According to the directive all obstructive undergrowth up to 8 cm diameter in breast height (1,3 meters above the ground) should be removed. Trees with a breast height diameter <8 are common in first thinning stands after cleaning, which is unprofitable for all links of the forest supply chain. Results from the field investigation, shows that 17 % of all remaining trees after cleaning are less than 8 cm breast height diameter. The history of forest management plays a crucial role for the result of undergrowth cleaning. If cleaning has been made once or twice earlier in the stand, the contractor`s job is easier since selection of main stems is already done. Otherwise the contractors made a god job according Mellanskog’s directive. The investigations show that there is a connection between average stem volume (solid under bark) and the cost of cleaning. If the average stem is small the cost will be high and vice versa. Result from the inquiry shows that the contractors understand well how the undergrowth cleaning should be done in theory, in practice, result shows that the contractors does not comply with the directive, i.e. to remove all obstructive undergrowth up to 8 cm diameter in breast height (according to the machine contractors). One positive observation is that the machine contractors have also experienced an obvious improvement of the undergrowth cleaning in the last years

Freedom near Lightcone and ANEC Saturation

Averaged Null Energy Conditions (ANECs) hold in unitary quantum field theories. In conformal field theories, ANECs in states created by the application of the stress tensor to the vacuum lead to three constraints on the stress-tensor three-point couplings, depending on the choice of polarization. The same constraints follow from considering two-point functions of the stress tensor in a thermal state and focusing on the contribution of the stress tensor in the operator product expansion (OPE). One can observe this in holographic Gauss-Bonnet gravity, where ANEC saturation coincides with the appearance of superluminal signal propagation in thermal states. We show that, when this happens, the corresponding generalizations of ANECs for higher-spin multi-stress tensor operators with minimal twist are saturated as well and all contributions from such operators to the thermal two-point functions vanish in the lightcone limit. This leads to a special near-lightcone behavior of the thermal stress-tensor correlators -- they take the vacuum form, independent of temperature.Comment: 36 page

A School-Based Exercise Intervention Program Increases Muscle Strength in Prepubertal Boys

This prospective controlled intervention study over 12 months evaluated the effect of exercise on muscular function, physical ability, and body composition in pre-pubertal boys. Sixty-eight boys aged 6–8 years, involved in a general school-based exercise program of 40 min per school day (200 min/week), were compared with 46 age-matched boys who participated in the general Swedish physical education curriculum of mean 60 min/week. Baseline and annual changes of body composition were measured by dual energy X-ray absorptiometry (DXA), stature, and body mass by standard equipments, isokinetic peak torque (PT) of the knee extensors, and flexors at 60 and 180 deg/sec by computerized dynamometer (Biodex) and vertical jump height (VJH) by a computerized electronic mat. The annual gain in stature and body mass was similar between the groups whereas the increase in total body and regional lean mass (P < .001) and fat mass (P < .001) was greater in the exercise group. The one-year gain in body mass-adjusted knee extensor and flexor PT at 180 deg/sec was significantly greater in the intervention group compared with the control group (P < .01, adjusted for age at baseline and P < .001, adjusted for age and muscle strength at baseline, resp.). There was no group difference in VJH. In conclusion, the increase in school-based physical education from 60 to 200 minutes per week enhances the development of lean body mass and muscle strength in pre-pubertal boys

Black hole bulk-cone singularities

Lorentzian correlators of local operators exhibit surprising singularities in theories with gravity duals. These are associated with null geodesics in an emergent bulk geometry. We analyze singularities of the thermal response function dual to propagation of waves on the AdS Schwarzschild black hole background. We derive the analytic form of the leading singularity dual to a bulk geodesic that winds around the black hole. Remarkably, it exhibits a boundary group velocity larger than the speed of light, whose dual is the angular velocity of null geodesics at the photon sphere. The strength of this singularity is controlled by the classical Lyapunov exponent associated with the instability of nearly bound photon orbits. In this sense, the bulk-cone singularity can be identified as the universal feature that encodes the ubiquitous black hole photon sphere in a dual holographic CFT. To perform the computation analytically, we express the two-point correlator as an infinite sum over Regge poles, and then evaluate this sum using WKB methods. We also compute the smeared correlator numerically, which in particular allows us to check and support our analytic predictions. We comment on the resolution of black hole bulk-cone singularities by stringy and gravitational effects into black hole bulk-cone "bumps". We conclude that these bumps are robust, and could serve as a target for simulations of black hole-like geometries in table-top experiments.Comment: 63 pages, 17 figure