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

Emerging Non-Anomalous Baryonic Symmetries in the AdS_5/CFT_4 Correspondence

We study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular VEVs, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We claim that these VEVs correspond to critical values of the B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold, the cone over F_0 and the C^3/Z_5 orbifold. For the first two examples, we study the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries and identify the expected Goldstone bosons and global strings in the infra-red. In doing so we confirm the claim that the emerging symmetries are indeed non-anomalous baryonic symmetries.Comment: 65 pages, 15 figures;v2: minor changes, published versio

Scattering Amplitudes and Toric Geometry

In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of well defined finite objects called on-shell diagrams drawn on disks. Furthermore it has been shown that the physical information of on-shell diagrams is encoded in the geometry of auxiliary algebraic varieties called the totally non negative Grassmannians. In this new formulation the infinite dimensional symmetry of the theory is manifest and many results, that are quite tricky to obtain in terms of the standard Lagrangian formulation of the theory, are instead manifest. In this paper, elaborating on previous results, we provide another picture of the scattering amplitudes in terms of toric geometry. In particular we describe in detail the toric varieties associated to an on-shell diagram, how the singularities of the amplitudes are encoded in some subspaces of the toric variety, and how this picture maps onto the Grassmannian description. Eventually we discuss the action of cluster transformations on the toric varieties. The hope is to provide an alternative description of the scattering amplitudes that could contribute in the developing of this very interesting field of research.Comment: 58 pages, 25 figures, typos corrected, a reference added, to be published in JHE

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

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table

N=2 solutions of massive type IIA and their Chern-Simons duals

We find explicit AdS4 solutions of massive type IIA with N=2 supersymmetry obtained deforming with a Roman mass the type IIA supersymmetric reduction of the M theory background AdS4 times M111. The family of solutions have SU(3) times SU(3) structure and isometry SU(3) times U(1)^2. They are conjectured to be dual to three-dimensional N=2 Chern-Simons theories with generic Chern-Simons couplings and gauge group ranks.Comment: 20 pages, 1 figure, comments and references adde

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

Weed Seed Bank Emergence across the Corn Belt

Field experiments, conducted from 1991 to 1994, generated information on weed seedbank emergence for 22 site-years from Ohio to Colorado and Minnesota to Missouri. Early spring seedbank densities were estimated through direct extraction of viable seeds from soil cores. Emerged seedlings were recorded periodically, as were daily values for air and soil temperature, and precipitation. Percentages of weed seedbanks that emerged as seedlings were calculated from seedbank and seedling data for each species, and relationships between seedbank emergence and microclimatic variables were sought. Fifteen species were found in 3 or more site-years. Average emergence percentages (and coefficients of variation) of these species were as follows: giant foxtail, 31.2 (84%); velvetleaf, 28.2 (66); kochia, 25.7 (79); Pennsylvania smartweed, 25.1 (65); common purslane, 15.4 (135); common ragweed, 15.0 (110); green foxtail, 8.5 (72); wild proso millet, 6.6 (104); hairy nightshade, 5.2 (62); common sunflower, 5.0 (26); yellow foxtail, 3.4 (67); pigweed species, 3.3 (103); common lambsquarters, 2.7 (111); wild buckwheat, 2.5 (63), and prostrate knotweed, 0.6 (79). Variation among site-years, for some species, could be attributed to microclimate variables thought to induce secondary dormancy in spring. For example, total seasonal emergence percentage of giant foxtail was related positively to the 1st date at which average daily soil temperature at 5 to 10 cm soil depth reached 16 C. Thus, if soil warmed before mid April, secondary dormancy was induced and few seedlings emerged, whereas many seedlings emerged if soil remained cool until June

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

Neutrino Masses, Baryon Asymmetry, Dark Matter and the Moduli Problem : A Complete Framework

Recent developments in string theory have led to "realistic" string compactifications which lead to moduli stabilization while generating a hierarchy between the Electroweak and Planck scales at the same time. However, this seems to suggest a rethink of our standard notions of cosmological evolution after the end of inflation and before the beginning of BBN. We argue that within classes of realistic string compactifications, there generically exists a light modulus with a mass comparable to that of the gravitino which generates a large late-time entropy when it decays. Therefore, all known mechanisms of generating the baryon asymmetry of the Universe in the literature have to take this fact into account. In this work, we find that it is still possible to naturally generate the observed baryon asymmetry of the Universe as well as light left-handed neutrino masses from a period of Affleck-Dine(AD) leptogenesis shortly after the end of inflation, in classes of realistic string constructions with a minimal extension of the MSSM below the unification scale (consisting only of right-handed neutrinos) and satisfying certain microscopic criteria described in the text. The consequences are as follows. The lightest left-handed neutrino is required to be virtually massless. The moduli (gravitino) problem can be naturally solved in this framework both within gravity and gauge mediation. The observed upper bound on the relic abundance constrains the moduli-matter and moduli-gravitino couplings since the DM is produced non-thermally within this framework. Finally, although not a definite prediction, the framework naturally allows a light right-handed neutrino and sneutrinos around the electroweak scale which could have important implications for DM as well as the LHC.Comment: 41 pages, no figures, journal version adde