Dimer models from mirror symmetry and quivering amoebae

Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume

Pomacytosis”—Semi-Extracellular Phagocytosis of Cyanobacteria by the Smallest Marine Algae

The smallest algae, less than 3 μm in diameter, are the most abundant eukaryotes of the World Ocean. Their feeding on planktonic bacteria of similar size is globally important but physically enigmatic. Tiny algal cells tightly packed with the voluminous chloroplasts, nucleus, and mitochondria appear to have insufficient organelle-free space for prey internalization. Here, we present the first direct observations of how the 1.3-μm algae, which are only 1.6 times bigger in diameter than their prey, hold individual Prochlorococcus cells in their open hemispheric cytostomes. We explain this semi-extracellular phagocytosis by the cell size limitation of the predatory alga, identified as the Braarudosphaera haptophyte with a nitrogen (N2)–fixing endosymbiont. Because the observed semi-extracellular phagocytosis differs from all other types of protistan phagocytosis, we propose to name it “pomacytosis” (from the Greek πώμα for “plug”)

On the Classification of Brane Tilings

We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most comprehensive study of such objects to date.Comment: 33 pages, 12 figures, 15 table

Integrability on the Master Space

It has been recently shown that every SCFT living on D3 branes at a toric Calabi-Yau singularity surprisingly also describes a complete integrable system. In this paper we use the Master Space as a bridge between the integrable system and the underlying field theory and we reinterpret the Poisson manifold of the integrable system in term of the geometry of the field theory moduli space.Comment: 47 pages, 20 figures, using jheppub.st

Survival through networks: the 'grip' of the administrative links in the Russian post-Soviet context

© 2014 Taylor & Francis. Based on an analysis of the post-Soviet transformation experience of four defence sector organizations in a Russian region where the defence sector occupies a substantial part of the local economy, this article develops a typology of network relationships: Grooved Inter-relationship Patterns (Gr’ip) networks and Fluid Inter-relationship Patterns (Fl’ip) networks. This typology can be applied to a range of transition/emerging market and low system trust contexts. Gr’ip networks, in this case, represent the persisting legacy of the Soviet command-administrative system. Fl’ip networks are here an attempt by the defence companies to link into the civilian supply chains of a developing market economy. This article argues that Gr’ip networks had and still have a crucial role to play in Russian enterprises’ survival and development

Counting Orbifolds

We present several methods of counting the orbifolds C^D/Gamma. A correspondence between counting orbifold actions on C^D, brane tilings, and toric diagrams in D-1 dimensions is drawn. Barycentric coordinates and scaling mechanisms are introduced to characterize lattice simplices as toric diagrams. We count orbifolds of C^3, C^4, C^5, C^6 and C^7. Some remarks are made on closed form formulas for the partition function that counts distinct orbifold actions.Comment: 69 pages, 9 figures, 24 tables; minor correction

Formation and Shaping of the Antirrhinum Flower through Modulation of the CUP Boundary Gene

Boundary domain genes, expressed within or around organ primordia, play a key role in the formation, shaping, and subdivision of planar plant organs, such as leaves. However, the role of boundary genes in formation of more elaborate 3D structures, which also derive from organ primordia, remains unclear. Here we analyze the role of the boundary domain gene CUPULIFORMIS (CUP) in formation of the ornate Antirrhinum flower shape. We show that CUP expression becomes cleared from boundary subdomains between petal primordia, most likely contributing to formation of congenitally fused petals (sympetally) and modulation of growth at sinuses. At later stages, CUP is activated by dorsoventral genes in an intermediary region of the corolla. In contrast to its role at organ boundaries, intermediary CUP activity leads to growth promotion rather than repression and formation of the palate, lip, and characteristic folds of the closed Antirrhinum flower. Intermediary expression of CUP homologs is also observed in related sympetalous species, Linaria and Mimulus, suggesting that changes in boundary gene activity have played a key role in the development and evolution of diverse 3D plant shapes

Factorization of Seiberg-Witten Curves with Fundamental Matter

We present an explicit construction of the factorization of Seiberg-Witten curves for N=2 theory with fundamental flavors. We first rederive the exact results for the case of complete factorization, and subsequently derive new results for the case with breaking of gauge symmetry U(Nc) to U(N1)xU(N2). We also show that integrality of periods is necessary and sufficient for factorization in the case of general gauge symmetry breaking. Finally, we briefly comment on the relevance of these results for the structure of N=1 vacua.Comment: 24 pages, 2 figure

Symmetries of Abelian Orbifolds

Using the Polya Enumeration Theorem, we count with particular attention to C^3/Gamma up to C^6/Gamma, abelian orbifolds in various dimensions which are invariant under cycles of the permutation group S_D. This produces a collection of multiplicative sequences, one for each cycle in the Cycle Index of the permutation group. A multiplicative sequence is controlled by its values on prime numbers and their pure powers. Therefore, we pay particular attention to orbifolds of the form C^D/Gamma where the order of Gamma is p^alpha. We propose a generalization of these sequences for any D and any p.Comment: 75 pages, 13 figures, 30 table

Brane Tilings and Specular Duality

We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.Comment: 42 pages, 16 figures, 5 table