Bending branes for DCFT in two dimensions

We consider a holographic dual model for defect conformal field theories (DCFT) in which we include the backreaction of the defect on the dual geometry. In particular, we consider a dual gravity system in which a two-dimensional hypersurface with matter fields, the brane, is embedded into a three-dimensional asymptotically Anti-de Sitter spacetime. Motivated by recent proposals for holographic duals of boundary conformal field theories (BCFT), we assume the geometry of the brane to be determined by Israel junction conditions. We show that these conditions are intimately related to the energy conditions for the brane matter fields, and explain how these energy conditions constrain the possible geometries. This has implications for the holographic entanglement entropy in particular. Moreover, we give exact analytical solutions for the case where the matter content of the brane is a perfect fluid, which in a particular case corresponds to a free massless scalar field. Finally, we describe how our results may be particularly useful for extending a recent proposal for a holographic Kondo model.Comment: 35 pages + appendices, 12 figures, v2: added references and a paragraph on negative tension solutions, v3: updated reference

Quantum Quenches in a Holographic Kondo Model

We study non-equilibrium dynamics and quantum quenches in a recent gauge/gravity duality model for a strongly coupled system interacting with a magnetic impurity with $SU(N)$ spin. At large $N$, it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS$_2$ and models the impurity screening. We study the time dependence of the condensate induced by quenches of the Kondo coupling. The timescale for equilibration is generically given by the lowest-lying quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large $N$ phase transition, we study the critical slowing down and obtain the combination of critical exponents $z\nu=1$. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form $\sim t^{-a}\sin(b\log t)$. This indicates the emergence of a discrete scale invariance.Comment: 23 pages + appendices, 11 figure

The functional genome of CA1 and CA3 neurons under native conditions and in response to ischemia

<p>Abstract</p> <p>Background</p> <p>The different physiological repertoire of CA3 and CA1 neurons in the hippocampus, as well as their differing behaviour after noxious stimuli are ultimately based upon differences in the expressed genome. We have compared CA3 and CA1 gene expression in the uninjured brain, and after cerebral ischemia using laser microdissection (LMD), RNA amplification, and array hybridization.</p> <p>Results</p> <p>Profiling in CA1 vs. CA3 under normoxic conditions detected more than 1000 differentially expressed genes that belong to different, physiologically relevant gene ontology groups in both cell types. The comparison of each region under normoxic and ischemic conditions revealed more than 5000 ischemia-regulated genes for each individual cell type. Surprisingly, there was a high co-regulation in both regions. In the ischemic state, only about 100 genes were found to be differentially expressed in CA3 and CA1. The majority of these genes were also different in the native state. A minority of interesting genes (e.g. inhibinbetaA) displayed divergent expression preference under native and ischemic conditions with partially opposing directions of regulation in both cell types.</p> <p>Conclusion</p> <p>The differences found in two morphologically very similar cell types situated next to each other in the CNS are large providing a rational basis for physiological differences. Unexpectedly, the genomic response to ischemia is highly similar in these two neuron types, leading to a substantial attenuation of functional genomic differences in these two cell types. Also, the majority of changes that exist in the ischemic state are not generated de novo by the ischemic stimulus, but are preexistant from the genomic repertoire in the native situation. This unexpected influence of a strong noxious stimulus on cell-specific gene expression differences can be explained by the activation of a cell-type independent conserved gene-expression program. Our data generate both novel insights into the relation of the quiescent and stimulus-induced transcriptome in different cells, and provide a large dataset to the research community, both for mapping purposes, as well as for physiological and pathophysiological research.</p