S-duality and 2d Topological QFT

We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure

Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index

We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a $\delta_\epsilon$-exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral by which the ${\cal N}=4$ superconformal index is expressed.Comment: 42+1 pages, 2 figures, JHEP style: v1.2.3 minor corrections, v4 major revision, conclusions essentially unchanged, v5 published versio

Counting Exceptional Instantons

We show how to obtain the instanton partition function of N=2 SYM with exceptional gauge group EFG using blow-up recursion relations derived by Nakajima and Yoshioka. We compute the two instanton contribution and match it with the recent proposal for the superconformal index of rank 2 SCFTs with E6, E7 global symmetry.Comment: 16 pages, references adde

Hilbert Series for Moduli Spaces of Two Instantons

The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKahler cone with a symmetry group U(2) \times G, where U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G_2 or F_4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure

Genomics of Aerobic Cellulose Utilization Systems in Actinobacteria

Cellulose degrading enzymes have important functions in the biotechnology industry, including the production of biofuels from lignocellulosic biomass. Anaerobes including Clostridium species organize cellulases and other glycosyl hydrolases into large complexes known as cellulosomes. In contrast, aerobic actinobacteria utilize systems comprised of independently acting enzymes, often with carbohydrate binding domains. Numerous actinobacterial genomes have become available through the Genomic Encyclopedia of Bacteria and Archaea (GEBA) project. We identified putative cellulose-degrading enzymes belonging to families GH5, GH6, GH8, GH9, GH12, GH48, and GH51 in the genomes of eleven members of the actinobacteria. The eleven organisms were tested in several assays for cellulose degradation, and eight of the organisms showed evidence of cellulase activity. The three with the highest cellulase activity were Actinosynnema mirum, Cellulomonas flavigena, and Xylanimonas cellulosilytica. Cellobiose is known to induce cellulolytic enzymes in the model organism Thermobifida fusca, but only Nocardiopsis dassonvillei showed higher cellulolytic activity in the presence of cellobiose. In T. fusca, cellulases and a putative cellobiose ABC transporter are regulated by the transcriptional regulator CelR. Nine organisms appear to use the CelR site or a closely related binding site to regulate an ABC transporter. In some, CelR also regulates cellulases, while cellulases are controlled by different regulatory sites in three organisms. Mining of genome data for cellulose degradative enzymes followed by experimental verification successfully identified several actinobacteria species which were not previously known to degrade cellulose as cellulolytic organisms

Quivers, YBE and 3-manifolds

We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and the invariance of the index under the duality is translated into the Yang-Baxter-type equation of a spin system defined on a "Z-invariant" lattice on T^2. When we compactify the gauge theory to 3d, Higgs the theory and then compactify further to 2d, the superconformal index reduces to an integral of quantum/classical dilogarithm functions. The saddle point of this integral unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The 3-manifold is obtained by gluing hyperbolic ideal polyhedra in H^3, each of which could be thought of as a 3d lift of the faces of the 2d bipartite graph.The same quantity is also related with the thermodynamic limit of the BPS partition function, or equivalently the genus 0 topological string partition function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also comment on brane realization of our theories. This paper is a companion to another paper summarizing the results.Comment: 61 pages, 16 figures; v2: typos correcte

M5-branes, toric diagrams and gauge theory duality

In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.Comment: 58 pages, 17 figures; v2: minor corrections, references adde

Expression Patterns of Protein Kinases Correlate with Gene Architecture and Evolutionary Rates

Protein kinase (PK) genes comprise the third largest superfamily that occupy ∼2% of the human genome. They encode regulatory enzymes that control a vast variety of cellular processes through phosphorylation of their protein substrates. Expression of PK genes is subject to complex transcriptional regulation which is not fully understood.Our comparative analysis demonstrates that genomic organization of regulatory PK genes differs from organization of other protein coding genes. PK genes occupy larger genomic loci, have longer introns, spacer regions, and encode larger proteins. The primary transcript length of PK genes, similar to other protein coding genes, inversely correlates with gene expression level and expression breadth, which is likely due to the necessity to reduce metabolic costs of transcription for abundant messages. On average, PK genes evolve slower than other protein coding genes. Breadth of PK expression negatively correlates with rate of non-synonymous substitutions in protein coding regions. This rate is lower for high expression and ubiquitous PKs, relative to low expression PKs, and correlates with divergence in untranslated regions. Conversely, rate of silent mutations is uniform in different PK groups, indicating that differing rates of non-synonymous substitutions reflect variations in selective pressure. Brain and testis employ a considerable number of tissue-specific PKs, indicating high complexity of phosphorylation-dependent regulatory network in these organs. There are considerable differences in genomic organization between PKs up-regulated in the testis and brain. PK genes up-regulated in the highly proliferative testicular tissue are fast evolving and small, with short introns and transcribed regions. In contrast, genes up-regulated in the minimally proliferative nervous tissue carry long introns, extended transcribed regions, and evolve slowly.PK genomic architecture, the size of gene functional domains and evolutionary rates correlate with the pattern of gene expression. Structure and evolutionary divergence of tissue-specific PK genes is related to the proliferative activity of the tissue where these genes are predominantly expressed. Our data provide evidence that physiological requirements for transcription intensity, ubiquitous expression, and tissue-specific regulation shape gene structure and affect rates of evolution

Measurement of the Z/gamma* + b-jet cross section in pp collisions at 7 TeV

The production of b jets in association with a Z/gamma* boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7 TeV and recorded by the CMS detector. The inclusive cross section for Z/gamma* + b-jet production is measured in a sample corresponding to an integrated luminosity of 2.2 inverse femtobarns. The Z/gamma* + b-jet cross section with Z/gamma* to ll (where ll = ee or mu mu) for events with the invariant mass 60 < M(ll) < 120 GeV, at least one b jet at the hadron level with pT > 25 GeV and abs(eta) < 2.1, and a separation between the leptons and the jets of Delta R > 0.5 is found to be 5.84 +/- 0.08 (stat.) +/- 0.72 (syst.) +(0.25)/-(0.55) (theory) pb. The kinematic properties of the events are also studied and found to be in agreement with the predictions made by the MadGraph event generator with the parton shower and the hadronisation performed by PYTHIA.Comment: Submitted to the Journal of High Energy Physic

Transcription Regulation of Sex-Biased Genes during Ontogeny in the Malaria Vector Anopheles gambiae

In Anopheles gambiae, sex-regulated genes are responsible for controlling gender dimorphism and are therefore crucial in determining the ability of female mosquitoes to transmit human malaria. The identification and functional characterization of these genes will shed light on the sexual development and maturation of mosquitoes and provide useful targets for genetic control measures aimed at reducing mosquito fertility and/or distorting the sex ratio