Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson Theory

In this paper we will discuss the effect of a having a boundary on the supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson (BLG) Theory. We will show that even though the supersymmetry and gauge invariance of the original BLG theory is broken due to the presence of a boundary, it restored by the addition of suitable boundary terms. In fact, to achieve the gauge invariance of this theory, we will have to introduce new boundary degrees of freedom. The boundary theory obeyed by these new boundary degrees of freedom will be shown to be a generalization of the gauged Wess-Zumino-Witten model, with the generators of the Lie algebra replaced by the generators of the Lie 3-algebra. The gauge and supersymmetry variations of the boundary theory will exactly cancel the boundary terms generated by the gauge and supersymmetric variations of the bulk theory.Comment: 15 pages, 0 figures, accepted for publication in JHE

Glutamatergic deficits and parvalbumin-containing inhibitory neurons in the prefrontal cortex in schizophrenia

<p>Abstract</p> <p>Background</p> <p>We have previously reported that the expression of the messenger ribonucleic acid (mRNA) for the NR2A subunit of the N-methyl-D-aspartate (NMDA) class of glutamate receptor was decreased in a subset of inhibitory interneurons in the cerebral cortex in schizophrenia. In this study, we sought to determine whether a deficit in the expression of NR2A mRNA was present in the subset of interneurons that contain the calcium buffer parvalbumin (PV) and whether this deficit was associated with a reduction in glutamatergic inputs in the prefrontal cortex (PFC) in schizophrenia.</p> <p>Methods</p> <p>We examined the expression of NR2A mRNA, labeled with a ³⁵S-tagged riboprobe, in neurons that expressed PV mRNA, visualized with a digoxigenin-labeled riboprobe via an immunoperoxidase reaction, in twenty schizophrenia and twenty matched normal control subjects. We also immunohistochemically labeled the glutamatergic axon terminals with an antibody against vGluT1.</p> <p>Results</p> <p>The density of the PV neurons that expressed NR2A mRNA was significantly decreased by 48-50% in layers 3 and 4 in the subjects with schizophrenia, but the cellular expression of NR2A mRNA in the PV neurons that exhibited a detectable level of this transcript was unchanged. In addition, the density of vGluT1-immunoreactive boutons was significantly decreased by 79% in layer 3, but was unchanged in layer 5 of the PFC in schizophrenia.</p> <p>Conclusion</p> <p>These findings suggest that glutamatergic neurotransmission via NR2A-containing NMDA receptors on PV neurons in the PFC may be deficient in schizophrenia. This may disinhibit the postsynaptic excitatory circuits, contributing to neuronal injury, aberrant information flow and PFC functional deficits in schizophrenia.</p

The Spin Foam Approach to Quantum Gravity

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.Comment: To appear in Living Reviews in Relativit