לוח שנה משולב

I will discuss a particular class of theories, which form a certain supersymmetric generalization of three-dimensional O(N) vector models. By combining tools of the conformal bootstrap with results obtained through supersymmetric localization, I will argue that theories in this class exhibit a symmetry enhancement at the infrared fixed point. This example is interesting because the putative infrared theory with no symmetry enhancement does not exhibit any obvious inconsistencies at first sight. Once the correct infrared theories have been identified, I will present a detailed numerical bootstrap analysis showing features (or "kinks") at positions that very nearly coincide with our expectation for these models. Moreover, I will present general numerical bounds in dimensions 3

We consider 4d N=1 superconformal theories on a cylinder. The partition function on this geometry computes the superconformal index, and can be obtained via the path integral with time direction compactified on a circle and periodic conditions for fermions. We will use an effective field theory approach to derive formulas for the asymptotics of such partition functions in the limit of very large circle and of very small circle. These limits are completely fixed in terms of coefficients of the Weyl anomaly (a,c). We will explain why supersymmetry is a necessary condition in 4d to establish these higher dimensional analogues of classic results in 2d CFTs. Finally we will discuss the extension to 6d and some applications.

Fear-related disorders are thought to reflect strong and persistent learned fear associations resulting from aberrant synaptic plasticity mechanisms. The basolateral amygdala (BLA) and the medial prefrontal cortex (mPFC) play a key role in the acquisition and extinction of fear memories. Strong reciprocal synaptic connections between these two regions are believed to play a role in the encoding of fear memories, but the contribution of these projection pathways to memory formation and maintenance remains elusive. We evaluated several optogenetic approaches for silencing presynaptic terminals. Surprisingly, we found that sustained activation of Arch, a light-gated proton pump that is commonly used for optogenetic silencing, paradoxically causes presynaptic calcium influx and neurotransmitter release. This increase in neurotransmission was mediated by presynaptic alkalization and calcium influx, and resulted in recruitment of local-circuit feed-forward inhibition, potentially confounding the interpretation of such experiments. We therefore established an optogenetic stimulation protocol that evokes long-term depression in BLA-mPFC synapses. Using this approach, we explored the role of the BLA-mPFC pathway in fear learning. We found that attenuation of synaptic strength in this pathway prior to fear conditioning leads to impaired learning. In mice that have already acquired the cued fear association, depotentiation of BLA-mPFC inputs prior to extinction training facilitated the extinction process. Our findings suggest a new role for the BLA-mPFC pathway not only in the in the acquisition but also the maintenance of learned associations and provide a framework for functional analysis of long-range projections.

When a polymer is quickly compressed it reaches a crumpled state that has attracted much attention as a model for DNA organization in the nucleus, conjectured to have a fractal struc-ture that has so far remained elusive. We will describe the relations between topology of knots, slow relaxation and the fast crumpling of the polymer, and propose a model for the col-lapse as a process similar to water drops condensing on a surface. Our model reproduces fea-tures of this state quantitatively, suggesting that the slow approach to scaling is related to a large dispersion in the sizes of ‘water drops’. Time permitting, we will present a model of unentangled directed polymers, whose universal properties are found to differ significantly from predictions of the best available theories. This suggests new directions in treating non-local topological constraints in polymer systems, a major open theoretical challenge.