A non-perturbative field theory approach for the Kondo effect: Emergence of an extra dimension and its implication for the holographic duality conjecture

Implementing Wilsonian renormalization group transformations in an iterative way, we develop a non-perturbative field theoretical framework, which takes into account all-loop quantum corrections organized in the $1/N$ expansion, where $N$ represents the flavor number of quantum fields. The resulting classical field theory is given by an effective Landau-Ginzburg theory for a local order parameter field, which appears in one-dimensional higher spacetime. We claim that such all-loop quantum corrections are introduced into an equation of motion for the order parameter field through the evolution in the emergent extra dimension. Based on this non-perturbative theoretical framework, we solve the Kondo effect, where the quantum mechanics problem in the projective formulation is mapped into a Landau-Ginzburg field theory for the hybridization order parameter field with an emergent extra dimension. We confirm the non-perturbative nature of this field theoretical framework. Intriguingly, we show that the Wilsonian renormalization group method can explain non-perturbative thermodynamic properties of an impurity consistent with the Bethe ansatz solutions. Finally, we speculate how our non-perturbative field theoretical framework can be connected with the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture.Comment: Completely rewritte

TNF-α inhibits glucose-induced insulin secretion in a pancreatic β-cell line (INS-1)

AbstractRecent studies suggest that TNF-α affects various biochemical and physiological processes which may be linked to the etiology of non-insulin-dependent diabetes mellitus (NIDDM). For example, TNF-α interferes with the signaling of the insulin receptor and the metabolism of glucose transporters. The possibility that TNF-α might directly reduce glucose-stimulated insulin secretion in pancreatic β-cells was examined by using an established pancreatic β-cell line (INS-1). TNF-α did not affect glucose-induced acute insulin secretion (30 min). However, over a longer time period (24 h), TNF-α decreased glucose-induced insulin secretion without affecting the total amount of insulin in the cell. In the presence of TNF-α levels of 0, 10, 100 and 1000 U/ml, the respective 20 mM glucose-induced insulin secretion was 1.736 ± 0.166, 1.750 ± 0.302, 1.550 ± 0.200, and 1.400 ± 0.112 mU/ml per 3 × 105 cells in 24 h