A Generating Function for Fatgraphs

We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi--classical computations, leading in particular to a closed formula corresponding to (genus zero, connected) trees.Comment: 24 pages, uses harvmac macro, 1 figure not included, Saclay preprint SPhT/92-16

Quantum intersection rings

We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.Comment: 73 p, uuencoded, uses harvmac in b mode, 6 figures include

Graphical chain models for the analysis of complex genetic diseases: an application to hypertension

A crucial task in modern genetic medicine is the understanding of complex genetic diseases. The main complicating features are that a combination of genetic and environmental risk factors is involved, and the phenotype of interest may be complex. Traditional statistical techniques based on lod-scores fail when the disease is no longer monogenic and the underlying disease transmission model is not defined. Different kinds of association tests have been proved to be an appropriate and powerful statistical tool to detect a candidate gene for a complex disorder. However, statistical techniques able to investigate direct and indirect influences among phenotypes, genotypes and environmental risk factors, are required to analyse the association structure of complex diseases. In this paper we propose graphical models as a natural tool to analyse the multifactorial structure of complex genetic diseases. An application of this model to primary hypertension data set is illustrated

Testing a quintessence model with CMBR peaks location

We show that a model of quintessence with exponential potential, which allows to obtain general exact solutions, can generate locations of CMBR peaks which are fully compatible with present observational dataComment: 7 pages, no figure

Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study

Using the density-matrix renormalization-group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to $S=9/2$. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly $c$, the sound velocity $v_{s}$, the anomalous dimension $x_{bulk}$, and the surface exponent $x_{s}$ of the anisotropic spin-$S$ Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entrop $S(L,l_{A},S)$ of the spin-$S$ Heisenberg chains satisfies the relation $S(L,l_{A},S)-S(L,l_{A},S-1)=1/(2S+1)$ for $S>3/2$ in the thermodynamic limit.Comment: 7 pages, 3 figs., 3 tables, to appear in PRB. Added new results for s>1/

Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions

In this work, we investigate an exactly solvable two-leg spin ladder with three-spin interactions. We obtain analytically the finite-size corrections of the low-lying energies and determine the central charge as well as the scaling dimensions. The model considered in this work has the same universality class of critical behavior of the XX chain with central charge c=1. By using the correlation matrix method, we also study the finite-size corrections of the Renyi entropy of the ground state and of the excited states. Our results are in agreement with the predictions of the conformal field theory.Comment: 10 pages, 6 figures, 2 table

M-Theory Through the Looking Glass: Tachyon Condensation in the E_8 Heterotic String

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to study the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_\xi gauges, and note the importance of logarithmic CFT in the context of tachyon condensation.Comment: 36 pages, 1 figur