Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.Comment: 49 pages, 6 figures; v2 refs added; v3 published versio

Annual Research Review: interparental conflict and youth psychopathology: an evidence review and practice focused update

The quality of the interparental relationship is recognized as an important influence on child and adolescent psychopathology. Historically, clinically-oriented research on this topic has focused on the impacts of parental divorce and domestic violence as primary interparental relationship influences on child outcomes, to the relative neglect of dimensional or qualitative features of the couple/interparental relationship for youth (child and adolescent) psychopathology. Recent research has highlighted that children are affected by attributes of interparental conflict, specifically how parents express and manage conflicts in their relationship, across a continuum of expressed severity and negativity – ranging from silence to violence. Further, new evidence highlights that children’s emotional, behavioral, social, academic outcomes and future interpersonal relationships are adversely affected by conflict between parents/carers whether adults are living together or not (i.e. married or separated), or where children are or are not genetically related to their rearing parents (e.g. adoption). We review evidence and present an integrated theoretical model, highlighting how children are affected by interparental conflict and what this evidence base means for effective intervention and prevention program development, as well as the development of possible cost-benefit models. Additionally, we review policy implications of this research and highlight some very recent examples of UK-based policy focusing on addressing the interparental relationship and its impact on youth psychopathology

M-theory on `toric' G_2 cones and its type II reduction

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extract the IIA reduction of M-theory on such backgrounds, as well as its type IIB dual. By studying the asymptotics of type II fields around the relevant loci, we confirm the interpretation of such backgrounds in terms of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find explicit, general expressions for the string coupling and R-R/NS-NS forms in the vicinity of these objects. Our solutions contain and generalize the field configurations relevant for certain models considered in recent work of Acharya and Witten.Comment: 45 pages, references adde

Leading strategies in competitive on-line prediction

We start from a simple asymptotic result for the problem of on-line regression with the quadratic loss function: the class of continuous limited-memory prediction strategies admits a "leading prediction strategy", which not only asymptotically performs at least as well as any continuous limited-memory strategy but also satisfies the property that the excess loss of any continuous limited-memory strategy is determined by how closely it imitates the leading strategy. More specifically, for any class of prediction strategies constituting a reproducing kernel Hilbert space we construct a leading strategy, in the sense that the loss of any prediction strategy whose norm is not too large is determined by how closely it imitates the leading strategy. This result is extended to the loss functions given by Bregman divergences and by strictly proper scoring rules.Comment: 20 pages; a conference version is to appear in the ALT'2006 proceeding

C^2/Z_n Fractional branes and Monodromy

We construct geometric representatives for the C^2/Z_n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of Harvey-Moore BPS algebras update

Supersymmetric Branes on AdS_5 x Y^{p,q} and their Field Theory Duals

We systematically study supersymmetric embeddings of D-brane probes of different dimensionality in the AdS_5xY^{p,q} background of type IIB string theory. The main technique employed is the kappa symmetry of the probe's worldvolume theory. In the case of D3-branes, we recover the known three-cycles dual to the dibaryonic operators of the gauge theory and we also find a new family of supersymmetric embeddings. The BPS fluctuations of dibaryons are analyzed and shown to match the gauge theory results. Supersymmetric configurations of D5-branes, representing domain walls, and of spacetime filling D7-branes (which can be used to add flavor) are also found. We also study the baryon vertex and some other embeddings which break supersymmetry but are nevertheless stable.Comment: LaTeX, 2 figures, 54 pages; v2: discussions sharpened at several points, new subsection and references adde

Parity nonconserving cold neutron-parahydrogen interactions

Three pion dominated observables of the parity nonconserving interactions between the cold neutrons and parahydrogen are calculated. The transversely polarized neutron spin rotation, unpolarized neutron longitudinal polarization, and photon-asymmetry of the radiative polarized neutron capture are considered. For the numerical evaluation of the observables, the strong interactions are taken into account by the Reid93 potential and the parity nonconserving interactions by the DDH model along with the two-pion exchange.Comment: 17 pages, 2 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