ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

Orientifolds and the Refined Topological String

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which computes refined open string amplitudes for branes wrapping Seifert three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new invariants of torus knots that generalize the Kauffman polynomials. At large N, the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined topological strings on an orientifold of the resolved conifold, generalizing the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define and solve refined Chern-Simons theory for all ADE gauge groups

Automated Analysis of Large-Scale NMR Data Generates Metabolomic Signatures and Links Them to Candidate Metabolites.

Identification of metabolites in large-scale <sup>1</sup> H NMR data from human biofluids remains challenging due to the complexity of the spectra and their sensitivity to pH and ionic concentrations. In this work, we tested the capacity of three analysis tools to extract metabolite signatures from 968 NMR profiles of human urine samples. Specifically, we studied sets of covarying features derived from principal component analysis (PCA), the iterative signature algorithm (ISA), and averaged correlation profiles (ACP), a new method we devised inspired by the STOCSY approach. We used our previously developed metabomatching method to match the sets generated by these algorithms to NMR spectra of individual metabolites available in public databases. On the basis of the number and quality of the matches, we concluded that ISA and ACP can robustly identify ten and nine metabolites, respectively, half of which were shared, while PCA did not produce any signatures with robust matches

Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles

In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the worldsheet then guarantees the decoupling at all loops. The holomorphic anomaly equations for open topological strings at one loop are also obtained and compared with the results of the Quillen formula

Extended Holomorphic Anomaly in Gauge Theory

The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special geometry. Modularity together with the (beta-dependent) gap structure at the various singular loci in the moduli space completely fixes the holomorphic ambiguity, also when the extension is non-trivial. In some cases, the theory at the orbifold radius, corresponding to beta=2, can be identified with an "orientifold" of the theory at beta=1. The various connections give hints for embedding the structure into the topological string.Comment: 25 page

General Omega Deformations from Closed String Backgrounds

In this note, an important extension to the recent construction of the fluxtrap background is presented. The fluxtrap is a closed string background based on the Melvin solution corresponding to the Omega deformation of flat space. In this note, we introduce the mechanisms to extend it from epsilon_1=-epsilon_2 in R to more general values of epsilon_1 and epsilon_2 in C.Comment: 12 pages. Typos corrected, some clarifications in text. Version accepted for publication in JHE

Calculations for Mirror Symmetry with D-branes

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum D-branes. A 4-d domain wall which is obtained in one region of closed string moduli space from wrapping a four-chain interpolating between two Lagrangian submanifolds is, for other values of the parameters, represented by a disk ending on a single Lagrangian.Comment: 42 page