Anomalous dimensions and splitting functions beyond the next-to-next-to-leading order

We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop (next-to-next-to-next-to-leading order, N^3LO) contributions to the flavour-singlet splitting functions and the gluon cusp anomalous dimension. We present first results, the moments N=2 and N=3, for the five-loop (N^4LO) non-singlet splitting functions.Comment: 10 pages, LaTeX (PoS style), 3 eps-figures. Contribution to the proceedings of `Loops & Legs 2018', St. Goar (Germany), April/May 201

Brane Tilings and Exceptional Collections

Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.Comment: 46 pages, 37 figures, JHEP3; v2: reference added, figure 13 correcte

Cosmogenic radionuclides on LDEF: An unexpected Be-10 result

Following the discovery of the atmospheric derived cosmogenic radionuclide Be-7 on the Long Duration Exposure Facility (LDEF), a search began for other known nuclides produced by similar mechanisms. None of the others have the narrow gamma-ray line emission of Be-7 decay which enabled its rapid detection and quantification. A search for Be-10 atoms on LDEF clamp plates using accelerator mass spectrometry is described. An unexpected result was obtained

New results on superconformal quivers

All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk'' del Pezzo models exist.Comment: 51 pages, many figure

Minimum-error discrimination between subsets of linearly dependent quantum states

A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal quantum states occurring with given a priori probabilities. A general analytical solution is obtained for N states that are restricted to a two-dimensional subspace of the Hilbert space of the system. The result for the special case of three arbitrary but linearly dependent states is applied to a variety of sets of three states that are symmetric and equally probable. It is found that, in this case, the minimum error probability for distinguishing one of the states from the other two is only about half as large as the minimum error probability for distinguishing all three states individually.Comment: Representation improved and generalized, references added. Accepted as a Rapid Communication in Phys. Rev.

Exceptional Collections and del Pezzo Gauge Theories

Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge groups (at the conformal point) in terms of the numbers of bifundamentals. We also provide a detailed analysis of four node quivers, examining when precisely mutations of the exceptional collection are related to Seiberg duality.Comment: 26 pages, 1 figure; v2 footnote 2 amended; v3 ref adde

A New Infinite Class of Quiver Gauge Theories

We construct a new infinite family of N=1 quiver gauge theories which can be Higgsed to the Y^{p,q} quiver gauge theories. The dual geometries are toric Calabi-Yau cones for which we give the toric data. We also discuss the action of Seiberg duality on these quivers, and explore the different Seiberg dual theories. We describe the relationship of these theories to five dimensional gauge theories on (p,q) 5-branes. Using the toric data, we specify some of the properties of the corresponding dual Sasaki-Einstein manifolds. These theories generically have algebraic R-charges which are not quadratic irrational numbers. The metrics for these manifolds still remain unknown.Comment: 29 pages, JHE

Seiberg Duality is an Exceptional Mutation

The low energy gauge theory living on D-branes probing a del Pezzo singularity of a non-compact Calabi-Yau manifold is not unique. In fact there is a large equivalence class of such gauge theories related by Seiberg duality. As a step toward characterizing this class, we show that Seiberg duality can be defined consistently as an admissible mutation of a strongly exceptional collection of coherent sheaves.Comment: 32 pages, 4 figures; v2 refs added, "orbifold point" discussion refined; v3 version to appear in JHEP, discussion of torsion sheaves improve

Powers of the vertex cover ideals

We describe a combinatorial condition on a graph which guarantees that all powers of its vertex cover ideal are componentwise linear. Then motivated by Eagon and Reiner's Theorem we study whether all powers of the vertex cover ideal of a Cohen-Macaulay graph have linear free resolutions. After giving a complete characterization of Cohen-Macaulay cactus graphs (i.e., connected graphs in which each edge belongs to at most one cycle) we show that all powers of their vertex cover ideals have linear resolutions

Mutant and chimeric recobinant plasminogen activatorsproduction in eukaryotic cellsand preliminary characterization

Mutant urokinase-type plasminogen activator (u-PA) genes and hybrid genes between tissue-type plasminogen activator (t-PA) and u-PA have been designed to direct the synthesis of new plasminogen activators and to investigate the structure-function relationship in these molecules. The following classes of constructs were made starting from cDNA encoding human t-PA or u-PA: 1) u-PA mutants in which the Arg156 and Lys158 were substituted with threonine, thus preventing cleavage by thrombin and plasmin; 2) hybrid molecules in which the NH2-terminal regions of t-PA (amino acid residues 1-67, 1-262, or 1-313) were fused with the COOH-terminal region of u-PA (amino acids 136-411, 139-411, or 195-411, respectively); and 3) a hybrid molecule in which the second kringle of t-PA (amino acids 173-262) was inserted between amino acids 130 and 139 of u-PA. In all cases but one, the recombinant proteins, produced by transfected eukaryotic cells, were efficiently secreted in the culture medium. The translation products have been tested for their ability to activate plasminogen after in situ binding to an insolubilized monoclonal antibody directed against urokinase. All recombinant enzymes were shown to be active, except those in which Lys158 of u-PA was substituted with threonine. Recombination of structural regions derived from t-PA, such as the finger, the kringle 2, or most of the A-chain sequences, with the protease part or the complete u-PA molecule did not impair the catalytic activity of the hybrid polypeptides. This observation supports the hypothesis that structural domains in t-PA and u-PA fold independently from one to another