Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime

We investigate the details of the bulk-boundary correspondence in Lorentzian signature anti-de Sitter space. Operators in the boundary theory couple to sources identified with the boundary values of non-normalizable bulk modes. Such modes do not fluctuate and provide classical backgrounds on which bulk excitations propagate. Normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition. They fluctuate and describe the Hilbert space of physical states. We provide an explicit, complete set of both types of modes for free scalar fields in global and Poincar\'e coordinates. For \ads{3}, the normalizable and non-normalizable modes originate in the possible representations of the isometry group \SL_L\times\SL_R for a field of given mass. We discuss the group properties of mode solutions in both global and Poincar\'e coordinates and their relation to different expansions of operators on the cylinder and on the plane. Finally, we discuss the extent to which the boundary theory is a useful description of the bulk spacetime.Comment: Standard LaTeX, 28 pages, 2 postscript figures. v2: References added. Substantial revision in section 3 of treatment of global modes; non-normalizable modes have arbitrary time dependence. Revised discussion of low-mass modes and puzzle raised re: coupling of the dual boundary operators. v3: unwanted paragraph removed. v4: Sec. 5.2 correcte

Bulk and Boundary Dynamics in BTZ Black Holes

Recently, the AdS/CFT conjecture of Maldacena has been investigated in Lorentzian signature by Balasubramanian et. al. We extend this investigation to Lorentzian BTZ black hole spacetimes, and study the bulk and boundary behaviour of massive scalar fields both in the non-extremal and extremal case. Using the bulk-boundary correspondence, we also evaluate the two-point correlator of operators coupling to the scalar field at the boundary of the spacetime, and find that it satisfies thermal periodic boundary conditions relevant to the Hawking temperature of the BTZ black hole.Comment: 22 pages, LaTeX file. v2: references added. v3: some typo corrections and minor clarification

Saturated and Unsaturated Intramyocellular Lipid Profiles and their Dynamic Changes after Exercise Intervention in Athletic Healthy Volunteers and Type 2 Diabetes Patients: an in vivo 1H-MRS study

Background: High levels of tri- and di-acylglycerols are found in skeletal muscle of endurance trained athletic healthy volunteers (Athl-HV) and type 2 diabetes patients (T2D), however their metabolic phenotypes are at opposite ends of insulin sensitivity and cardiometabolic risk. Here we investigated if intramyocellular lipid saturation may constitute a previously unknown determinant of cardiometabolic risk. Secondly, we explored if deconditioning/exercise training impacts on intramyocellular lipid saturation in Athl-HV/T2D, respectively. Methods: Age matched male Athl-HV and T2D were enrolled. Athl-HV performed endurance training ≥5 years, actively training ≥360 minutes/week; T2D performed ≤150 min exercise/week. Bike-cardiopulmonary exercise testing (CPET), blood sampling for insulin sensitivity (HOMA2-IR*) and single voxel 1H-magnetic resonance spectroscopy (1H-MRS) of the right vastus lateralis were performed in all at baseline and after exercise intervention (4 week deconditioning in Athl-HV and investigator-supervised bike training at ≥65% of baseline peakVO2, 5 hours/week x 8 weeks in T2D). 1H-MRS was acquired on 3T Philips Achieva with a 16-channel coil, point-resolved spectroscopy, variable pulse power and optimized relaxation delay water suppression. 1H-MRS data were analysed in LCModel. Intensities of total, saturated and unsaturated intra- and extra-myocellular lipids and creatine resonance lines were normalized to internal water. Fractional lipid mass (fLM) [lipid/(lipid+water)] as well as fractions of saturated (fSL) (saturated/total) and unsaturated (fUL) (unsaturated/total) lipid components were calculated. Data were analysed by paired/unpaired t tests and shown as mean±SEM. Significance was set at p<0.05. Results: Deconditioning/exercise traning led to significant weight gain/loss in Athl-HV/T2D, respectively. Peak VO2 significantly decreased in Athl-HV and increased in T2D. Insulin sensitivity was higher in Athl-HV than T2D (Table 1). Higher fLM was found in the skeletal muscle of T2D compared to Athl-HV, at baseline (p=0.002) and after exercise intervention (p=0.03), Figure 1A. At baseline, T2D had a trend for lower fSL and higher fUL compared to Athl-HV (80±8 vs 86±1% and 19±3 vs 14±7%, p=0.07 for both). Neither fSL nor fUL changed with deconditioning in Athl-HV. However, exercise training resulted in a significant increase in fSL (80±8 to 88±3%) and reciprocal decrease in fUL (19±9 to 12±3%) in T2D (both p=0.004), Figure 1B and C. Conclusion: We demonstrate differences in total amount and saturation of intramyocellular lipids between Athl-HV and T2D. Further, intramyocellular lipid saturation is modulated by exercise training in T2D, to mirror the phenotype seen in Athl-HV, implying that this may be either an independent or an earlier marker of improved cardio-metabolic health than insulin sensitivity