The puzzle of bulk conformal field theories at central charge c=0

Non-trivial critical models in 2D with central charge c=0 are described by Logarithmic Conformal Field Theories (LCFTs), and exhibit in particular mixing of the stress-energy tensor with a "logarithmic" partner under a conformal transformation. This mixing is quantified by a parameter (usually denoted b), introduced in [V. Gurarie, Nucl. Phys. B 546, 765 (1999)], and which was first thought to play the role of an "effective" central charge. The value of b has been determined over the last few years for the boundary versions of these models: $b_{\rm perco}=-5/8$ for percolation and $b_{\rm poly} = 5/6$ for dilute polymers. Meanwhile, the existence and value of $b$ for the bulk theory has remained an open problem. Using lattice regularization techniques we provide here an "experimental study" of this question. We show that, while the chiral stress tensor has indeed a single logarithmic partner in the chiral sector of the theory, the value of b is not the expected one: instead, b=-5 for both theories. We suggest a theoretical explanation of this result using operator product expansions and Coulomb gas arguments, and discuss the physical consequences on correlation functions. Our results imply that the relation between bulk LCFTs of physical interest and their boundary counterparts is considerably more involved than in the non-logarithmic case.Comment: 5 pages, published versio

Reappraisal of anoxic spreading depolarization as a terminal event during oxygen–glucose deprivation in brain slices in vitro

International audienceAnoxic spreading depolarization (aSD) has been hypothesized as a terminal event during oxygen-glucose deprivation (OGD) in submerged cortical slices in vitro. However, mechanical artifacts caused by aSD-triggered edema may introduce error in the assessment of neuronal viability. Here, using continuous patch-clamp recordings from submerged rat cortical slices, we first confirmed that vast majority of L4 neurons permanently lost their membrane potential during OGD-induced aSD. In some recordings, spontaneous transition from whole-cell to outside out configuration occurred during or after aSD, and only a small fraction of neurons survived aSD with reperfusion started shortly after aSD. Secondly, to minimize artifacts caused by OGD-induced edema, cells were short-term patched following OGD episodes of various duration. Nearly half of L4 cells maintained membrane potential and showed the ability to spike-fire if reperfusion started less than 10 min after aSD. The probability of finding live neurons progressively decreased at longer reperfusion delays at a rate of about 2% per minute. We also found that neurons in L2/3 show nearly threefold higher resistance to OGD than neurons in L4. Our results suggest that in the OGD ischemia model, aSD is not a terminal event, and that the "commitment point" of irreversible damage occurs at variable delays, in the range of tens of minutes, after OGD-induced aSD in submerged cortical slices. Duration of ischemia is the key factor determining neuronal survival, neurological, and behavioral outcome. During global brain ischemia caused by cardiac arrest, irreversible loss of brain function and legal death are conventionally thought to occur within 5-10 min of cardiac arrest 1. Paradoxically, however, neuronal function can be restored even after much longer periods of global ischemia under several experimental settings including extracorporeal reperfusion with special cytoprotective reperfusate up to 4 h after cardiac arrest in pigs 2 or maintenance of rat brain slices that were prepared 1-6 h after cardiac arrest 3 , or after 30 min middle cerebral artery occlusion 4 , in ACSF. These observations raised the hypothesis that neurons may survive much longer episodes of ischemia than traditionally thought, thus opening questions for further research on the possibility of expanding the time window for resuscitation. Development of brain injury during ischemia proceeds through the initial phase of compensation, during which brain activity ceases but neurons maintain their membrane potential, and recovery of cardiovascular function restores brain activity without major damage to the brain 1,5,6. Passage to the decompensation phase is associated with a wave of collective and nearly complete neuronal depolarization, so-called anoxic spreading depolarization (aSD) occurring at ~ 5 min after the onset of ischemia 5,7,8. Generation of aSD is caused by depletion of intracellular reserves of energy metabolites, loss of function of the energy-dependent active ion transporters and rupture in transmembrane ionic gradients 5,7,8. aSD is a highly energy-demanding event which severely aggravates metabolic status 9. Considerable evidence indicates that aSD is the key ischemic event that triggers cascades of intracellular reactions leading to acute and delayed neuronal death 5,7,8. Similarly, periinfarct depolarizations (PIDs) severely compromise the metabolic state in the penumbra and cause expansion of the ischemic core during the development of the focal ischemic injury 10. The oxygen-glucose deprivation (OGD) model of an ischemia-like condition has been extensively used to explore acute changes in neuronal function during metabolic insult in brain slices in vitro. In this model, metabolite deprivation causes a series of events largely recapitulating the development of ischemic injury OPE