Baryonic Generating Functions

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.Comment: 44 pages, 7 figures; fonts change

A high-throughput, straightforward procedure for biomonitoring organomercury species in human hair

Mercury is a pervasive and concerning pollutant due to its toxicity, mobility, and tendency to biomagnify in aquatic and terrestrial ecosystems. Speciation analysis is crucial to assess exposure and risks associated with mercury, as different mercury species exhibit varying properties and toxicities. This study aimed at developing a selective detection method for organic mercury species in a non-invasive biomonitoring matrix like human hair. The method is based on frontal chromatography (FC) in combination with inductively coupled plasma mass spectrometry (ICP-MS), using a low pressure, homemade, anion exchange column inserted in a standard ICP-MS introduction system, without requiring high-performance liquid chromatography (HPLC) hyphenation. In addition to the extreme simplification and cost reduction of the chromatographic equipment, the proposed protocol involves a fast, streamlined and fully integrated sample preparation process (in contrast to existing methods): the optimized procedure features a 15-min ultrasonic assisted extraction procedure and 5 min analysis time. Consequently, up to 100 samples could be analyzed daily, making the method highly productive and suitable for large-scale screening programs in public and environmental health. Moreover, the optimized procedure enables a limit of detection (LOD) of 5.5 μg/kg for a 10 mg hair microsample. All these features undeniably demonstrate a significant advancement in routine biomonitoring practices. To provide additional evidence, the method was applied to forty-nine human hair samples from individuals with varying dietary habits successfully finding a clear correlation between methylmercury levels (ranging from 0.02 to 3.2 mg/kg) in hair and fish consumption, in line with previous literature data

Brane Tilings and M2 Branes

Brane tilings are efficient mnemonics for Lagrangians of N=2 Chern-Simons-matter theories. Such theories are conjectured to arise on M2-branes probing singular toric Calabi-Yau fourfolds. In this paper, a simple modification of the Kasteleyn technique is described which is conjectured to compute the three dimensional toric diagram of the non-compact moduli space of a single probe. The Hilbert Series is used to compute the spectrum of non-trivial scaling dimensions for a selected set of examples.Comment: 47 pages, 23 figure

A-D-E Quivers and Baryonic Operators

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The string theory analysis predicts that the number and the order of the fixed points of Gamma acting on S^2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by developing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks. We also find that the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1, references adde

Comments on Anomalies and Charges of Toric-Quiver Duals

We obtain a simple expression for the triangle `t Hooft anomalies in quiver gauge theories that are dual to toric Sasaki-Einstein manifolds. We utilize the result and simplify considerably the proof concerning the equivalence of a-maximization and Z-minimization. We also resolve the ambiguity in defining the flavor charges in quiver gauge theories. We then compare coefficients of the triangle anomalies with coefficients of the current-current correlators and find perfect agreement.Comment: 22 pages, 3 figure

Counting Chiral Operators in Quiver Gauge Theories

We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number of D-branes. Explicit formulae are given for few examples, including C^3/Z_3, F_0, and dP_1.Comment: 75 pages, 22 figure

Deformations of conformal theories and non-toric quiver gauge theories

We discuss several examples of non-toric quiver gauge theories dual to Sasaki-Einstein manifolds with U(1)^2 or U(1) isometry. We give a general method for constructing non-toric examples by adding relevant deformations to the toric case. For all examples, we are able to make a complete comparison between the prediction for R-charges based on geometry and on quantum field theory. We also give a general discussion of the spectrum of conformal dimensions for mesonic and baryonic operators for a generic quiver theory; in the toric case we make an explicit comparison between R-charges of mesons and baryons.Comment: 51 pages, 12 figures; minor corrections in appendix B, published versio

R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization

We conjecture a general formula for assigning R-charges and multiplicities for the chiral fields of all gauge theories living on branes at toric singularities. We check that the central charge and the dimensions of all the chiral fields agree with the information on volumes that can be extracted from toric geometry. We also analytically check the equivalence between the volume minimization procedure discovered in hep-th/0503183 and a-maximization, for the most general toric diagram. Our results can be considered as a very general check of the AdS/CFT correspondence, valid for all superconformal theories associated with toric singularities.Comment: 43 pages, 17 figures; minor correction

QCD and String Theory

This talk begins with some history and basic facts about string theory and its connections with strong interactions. Comparisons of stacks of Dirichlet branes with curved backgrounds produced by them are used to motivate the AdS/CFT correspondence between superconformal gauge theory and string theory on a product of Anti-de Sitter space and a compact manifold. The ensuing duality between semi-classical spinning strings and long gauge theory operators is briefly reviewed. Strongly coupled thermal SYM theory is explored via a black hole in 5-dimensional AdS space, which leads to explicit results for its entropy and shear viscosity. A conjectured universal lower bound on the viscosity to entropy density ratio, and its possible relation to recent results from RHIC, are discussed. Finally, some available results on string duals of confining gauge theories are briefly reviewed.Comment: 12 pages, prepared for the Proceedings of the 2005 Lepton-Photon Symposium; v2: minor revisions, references added, the version to appear in the proceeding

A note on dimer models and McKay quivers

We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng, He, Kennaway and Vafa.Comment: 25 pages, 35 figures. v3:completely rewritte