The D^{10} R^4 term in type IIB string theory

The modular invariant coefficient of the D^{2k} {\cal{R}}^4 term in the effective action of type IIB superstring theory is expected to satisfy Poisson equation on the fundamental domain of SL(2,Z). Under certain assumptions, we obtain the equation satisfied by D^{10} {\cal{R}}^4 using the tree level and one loop results for four graviton scattering in type II string theory. This leads to the conclusion that the perturbative contributions to D^{10} {\cal{R}}^4 vanish above three loops, and also predicts the coefficients at two and three loops.Comment: 12 pages, LaTe

Vertex Operators for Super Yang-Mills and Multi D-Branes in Green-Schwarz Superstring

We study vertex operators for super Yang-Mills and multi D-branes in covariant form using Green-Schwarz formalism. We introduce the contact terms naturally and prove space-time supersymmetry and gauge invariance. The nonlinear realization of broken supersymmetry in the presence of D-branes is also discussed. The shift of fermionic coordinate \delta^{(-)}\Psi =\eta becomes exact symmetry of D-brane in the static gauge, where $\eta$ is a constant spinor in U(1) direction.Comment: Latex, 16 page

An algorithmic approach to resolutions

We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modified to construct minimal projective resolutions of linear modules over Koszul algebras

Vacuum Values for Auxiliary String Fields

Auxiliary string fields are introduced in light-cone gauge string field theory in order to express contact interactions as contractions of cubic vertices. The auxiliary field in the purely closed-string bosonic theory may be given a non-zero expectation value, leading to a phase in which world-sheets have boundaries.Comment: 13 pages, DAMTP/94-2

Connections between M-theory and superstrings

This article reviews the non-perturbative structure of certain higher derivative terms in the type II string theory effective action and their connection to one-loop effects in eleven-dimensional supergravity compactified on a torus. New material is also included that was not presented in the talks.Comment: 24 pages LaTeX. Based on talks given at various conferences. To be published in the proceedings of the 1997 Advanced Study Institute on Strings, Branes and Dualities, Cargese, Franc

The Influence of World-Sheet Boundaries on Critical Closed String Theory

This paper considers interactions between closed strings and open strings satisfying either Neumann or constant (point-like) Dirichlet boundary conditions in a BRST formalism in the critical dimension. With Neumann conditions this reproduces the well-known stringy version of the Higgs mechanism. With Dirichlet conditions the open-string states correspond to either auxiliary or Lagrange multiplier target-space fields and their coupling to the closed-string sector leads to constraints on the closed-string spectrum.Comment: 15 pages, QMW-92-18;NI9201

Effects of D-instantons

Scattering of fundamental states of type IIB supergravity and superstring theory is discussed at low orders in perturbation theory in the background of a D-instanton. The integration over fermionic zero modes in both the low energy supergravity and in the string theory leads to explicit nonperturbative terms in the effective action. These include a single instanton correction to the known tree-level and one-loop $R^4$ interactions. The `spectrum' of multiply-charged D-instantons is deduced by T-duality in nine dimensions from multiply-wound world-lines of marginally-bound D-particles. This, and other clues, lead to a conjectured SL(2,Z) completion of the $R^4$ terms which suggests that they are not renormalized by perturbative corrections in the zero-instanton sector beyond one loop. The string theory unit-charged D-instanton gives rise to point-like effects in fixed-angle scattering, raising unresolved issues concerning distance scales in superstring theory.Comment: 31 pages, 6 figures, Latex, Reference added, corrected coefficients in expansion of generalized Eisenstein series in equation 66 now agree with hep-th/970414

Epidemiological information in sheep health management

We use epidemiology whenever we consider the management of sheep health. To measure a disease, we need a precise and unique case definition and we often use diagnostic tests to assist in defining a disease. Diagnostic tests are not always accurate. Thus, it is necessary to consider the decisions that will be taken, based on the result of testing, in order to decide the most useful approach to interpret a test based on its test sensitivity and specificity and the prevalence of the disease in a flock. This is particularly important when decisions on culling or selection of sheep to attain, e.g. freedom from disease, are made on the basis of test results. Infectious diseases spread within and between flocks in a variety of ways; brought-in sheep are the most likely source for introduction of a new pathogen or strain of a pathogen. When a pathogen enters a naïve flock, it spreads through susceptible sheep and persists in the flock, whilst there are susceptible sheep that can be infected. Pathogens use a variety of techniques to persist, including changes in the pathogen itself, alterations in infected hosts enabling them to remain infectious for prolonged periods or to be re-infected, persistence in other host species or in the environment. We need to consider these strategies to decide whether elimination or control of a particular pathogen is more likely to be effective. Whatever the flock control strategy, treatment of diseased individuals is essential for their welfare and can also protect the rest of the flock, if treatment reduces the infectious period. Decisions on management of disease are based on our knowledge of the flock and its management and the evidence base for various control strategies. There are now formal techniques for evaluating the evidence base that can assist in evaluating evidence. One area where we need to evaluate evidence is on cause. It is not possible to prove anything, but we can use the weight of evidence to evaluate likely cause. There are nine aspects of association with which we can evaluate a piece of evidence; these are: strength, consistency, specificity, temporality, dose–response, plausibility, coherence, experiment and analogy

Anomalies, D-flatness and Small Instantons

Recently, Witten has proposed a mechanism for symmetry enhancement in $SO(32)$ heterotic string theory, where the singularity obtained by shrinking an instanton to zero size is resolved by the appearance of an $Sp(1)$ gauge symmetry. In this short letter, we consider spacetime constraints from anomaly cancellation in six dimensions and D-flatness and demonstrate a subtlety which arises in the moduli space when many instantons are shrunk to zero size.Comment: 8 pages, harvma