Abstract:
We investigated the effects of PGC-1α (peroxisome proliferator-activated receptor γ coactivator-1α) overexpression on the oxidative capacity of human skeletal muscle cells ex vivo. PGC-1α overexpression increased the oxidation rate of palmitic acid and mRNA expression of genes regulating lipid metabolism, mitochondrial biogenesis, and function in human myotubes. Basal and insulin-stimulated deoxyglucose uptake were decreased, possibly due to upregulation of PDK4 mRNA. Expression of fast fiber-type gene marker (MHCIIa) was decreased. Compared to skeletal muscle in vivo, PGC-1α overexpression increased expression of several genes, which were downregulated during the process of cell isolation and culturing. In conclusion, PGC-1α overexpression increased oxidative capacity of cultured myotubes by improving lipid metabolism, increasing expression of genes involved in regulation of mitochondrial function and biogenesis, and decreasing expression of MHCIIa. These results suggest that therapies aimed at increasing PGC-1α expression may have utility in treatment of obesity and obesity-related diseases.

Abstract:
We investigated the effects of PGC-1α (peroxisome proliferator-activated receptor γ coactivator-1α) overexpression on the oxidative capacity of human skeletal muscle cells ex vivo. PGC-1α overexpression increased the oxidation rate of palmitic acid and mRNA expression of genes regulating lipid metabolism, mitochondrial biogenesis, and function in human myotubes. Basal and insulin-stimulated deoxyglucose uptake were decreased, possibly due to upregulation of PDK4 mRNA. Expression of fast fiber-type gene marker (MHCIIa) was decreased. Compared to skeletal muscle in vivo, PGC-1α overexpression increased expression of several genes, which were downregulated during the process of cell isolation and culturing. In conclusion, PGC-1α overexpression increased oxidative capacity of cultured myotubes by improving lipid metabolism, increasing expression of genes involved in regulation of mitochondrial function and biogenesis, and decreasing expression of MHCIIa. These results suggest that therapies aimed at increasing PGC-1α expression may have utility in treatment of obesity and obesity-related diseases. 1. Introduction The genesis of obesity is multifactorial. However, there is evidence that reduced energy expenditure and in particular reduced capacity to utilise fat for metabolic fuel are important factors, particularly in the weight reduced state [1] PGC-1α (peroxisome proliferator-activated receptor γ coactivator-1α) is a transcriptional coactivator initially isolated from brown adipose tissue [2], but now known to be abundant in many metabolically active tissues, such as skeletal muscle, liver, heart, and brain, where PGC-1α plays a major role in transduction of nutritional and physiological stimuli to transcriptional metabolic and contractile responses [2, 3]. Among many transcription factors coactivated by PGC-1α are nuclear respiratory factors (NRF1/2) [4], myocyte enhancer factor-2 (MEF2) [4], and several members of nuclear hormone receptors, including peroxisome proliferator-activated receptor (PPAR) subtypes—a family of lipid activated nuclear hormone receptors that play a key role in mediating adaptive regulation of muscle fatty acid oxidation [5]. The most common function of PGC-1α across tissues is regulation of mitochondrial physiology, but in addition, this family of coactivators controls separate, tissue-specific biological programs. In liver, expression of PGC-1α is strongly induced by fasting and stimulates hepatic gluconeogenesis and ketogenesis [6, 7]; in heart, it is a powerful stimulant of mitochondrial gene expression and biogenesis [8],

Abstract:
We start by giving a brief introduction to string theory with emphasis on the example of the bosonic string. In order to fully appreciate string theory it is necessary to study the dynamics of the surface that the string traces out when moving in space-time. This is described by what is known as conformal field theory, which is the subject of chapter two. After this digression we return to string theory to give some insight into how the results of the articles contained in this thesis could provide with interesting ingredients for constructions of realistic string theories. This is also continued on to some extent in chapter seven and eight. The articles in this thesis are discussing mainly two subjects, gauged WZNW models and affine branching functions. The background for those issues is given in chapter seven and eight. In the articles contained in this thesis we use two major tools. First affine Lie algebras and its representation theory, and secondly BRST quantization. In chapter four and five we deal with affine Lie algebras, and in chapter six we try to illuminate some issues on BRST quantization.

Abstract:
We consider the supersymmetric WZNW model gauged in a manifestly supersymmetric way. We find the BRST charge and the necessary condition for nilpotency. In the BRST framework the model proves to be a Lagrangian formulation of the supersymmetric coset construction, known as the N=1 Kazama-Suzuki coset construction.

Abstract:
We compute branching functions of $G/H$ coset models using a BRST invariant branching function formulae, i.e. a branching function that respects a BRST invariance of the model. This ensures that only the coset degrees of freedom will propagate. We consider $G/H$ for rank$(G/H)=0$ models which includes the Kazama-Suzuki construction, and $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ models. Our calculations here confirm in part previous results for those models which have been obtained under an assumption in a free field approach. We also consider $G_{k_1}\times H_{k_2}/H_{k_1+k_2}$, where $H$ is a subgroup of $G$, and $\prod_{a=1}^mG_{k_a}/G_{\sum_{a=1}^nk_a}$, whose branching functions, to our knowledge, has not been calculated before.

Abstract:
We here give a first indication that there exists a Seiberg-Witten curve for SU(N) Seiberg-Witten theory with matter transforming in the totally antisymmetric rank three tensor representation. We present a derivation of the leading order hyperelliptic approximation of a curve for this case. Since we are only interested in the asymptotic free theory we are restricted to $N=6,7,8$. The derivation is carried out by reversed engineering starting from the known form of the prepotential at tree level. We also predict the form of the one instanton correction to the prepotential.

Abstract:
We study the cohomology arising in the BRST formulation of G/H gauged WZNW models, i.e. in which the states of the gauged theory are projected out from the ungauged one by means of a BRST condition. We will derive for a general simple group $H$ with arbitrary level, conditions for which the cohomology is non-trivial. We show, by introducing a small perturbation due to Jantzen, in the highest weights of the representations, how states in the cohomology, "singlet pairs", arise from unphysical states, "Kugo-Ojima quartets", as the perturbation is set to zero. This will enable us to identify and construct states in the cohomology. The ghost numbers that will occur are $\pm p$, with $p$ uniquely determined by the representations of the algebras involved. Our construction is given in terms of the current modes and relies on the explicit form of highest weight null-states given by Malikov, Feigen and Fuchs.

Abstract:
WZNW models, especially gauged WZNW models, are important in the study of conformal field theories. Karabali and Schnitzer initiated the study of the BRST cohomology of a WZNW model gauged by an anomaly free vector sub-group and results were given for abelian sub-groups. This result was generalized to non-abelian sub-groups for a specific set of representations \cite{HR1}. The subject of this talk is the analysis of arbitrary representations \cite{HR2,Hw}.

Abstract:
We consider a BRST approach to G/H coset WZNW models, {\it i.e.} a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the the BRST cohomology. This will reveal a remarkable connection between integrable representations and a class of non-integrable representations for negative levels. The latter representations are also connected to string theories based on non-compact WZNW models. The partition functions of G/H cosets are also considered. The BRST approach enables a covariant construction of these, which does not rely on the decomposition of G as $G/H\times H$. We show that for the well-studied examples of $SU(2)_k \times SU(2)_1/SU(2)_{k+1}$ and $SU(2)_k/U(1)$, we exactly reproduce the previously known results.