Conformal Field Theory and Hyperbolic Geometry

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic length, we motivate a reformulation of the basic equation of conformal covariance. The scale factors gain a new, physical interpretation. We exhibit a fully factored form for the three-point function. A doubly-infinite discrete series of central charges with limit c=-2 is discovered. A correspondence between the anomalous dimension and the angle of certain hyperbolic figures emerges. Note: email after 12/19: [email protected]: 7 pages (PlainTeX

Fredholm Determinants, Differential Equations and Matrix Models

Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is a union of open intervals. The emphasis is on the determinants thought of as functions of the end-points of these intervals. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as phi and psi satisfy a certain type of differentiation formula. There is also an exponential variant of this analysis which includes the circular ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only the abstract and decreases length of typeset versio

Bosonization of non-relativstic fermions in 2-dimensions and collective field theory

We revisit bosonization of non-relativistic fermions in one space dimension. Our motivation is the recent work on bubbling half-BPS geometries by Lin, Lunin and Maldacena (hep-th/0409174). After reviewing earlier work on exact bosonization in terms of a noncommutative theory, we derive an action for the collective field which lives on the droplet boundaries in the classical limit. Our action is manifestly invariant under time-dependent reparametrizations of the boundary. We show that, in an appropriate gauge, the classical collective field equations imply that each point on the boundary satisfies Hamilton's equations for a classical particle in the appropriate potential. For the harmonic oscillator potential, a straightforward quantization of this action can be carried out exactly for any boundary profile. For a finite number of fermions, the quantum collective field theory does not reproduce the results of the exact noncommutative bosonization, while the latter are in complete agreement with the results computed directly in the fermi theory.Comment: references added and typos corrected; 21 pages, 3 figures, eps

Haloperidol and Ziprasidone for Treatment of Delirium in Critical Illness

BACKGROUND: There are conflicting data on the effects of antipsychotic medications on delirium in patients in the intensive care unit (ICU). METHODS: In a randomized, double-blind, placebo-controlled trial, we assigned patients with acute respiratory failure or shock and hypoactive or hyperactive delirium to receive intravenous boluses of haloperidol (maximum dose, 20 mg daily), ziprasidone (maximum dose, 40 mg daily), or placebo. The volume and dose of a trial drug or placebo was halved or doubled at 12-hour intervals on the basis of the presence or absence of delirium, as detected with the use of the Confusion Assessment Method for the ICU, and of side effects of the intervention. The primary end point was the number of days alive without delirium or coma during the 14-day intervention period. Secondary end points included 30-day and 90-day survival, time to freedom from mechanical ventilation, and time to ICU and hospital discharge. Safety end points included extrapyramidal symptoms and excessive sedation. RESULTS: Written informed consent was obtained from 1183 patients or their authorized representatives. Delirium developed in 566 patients (48%), of whom 89% had hypoactive delirium and 11% had hyperactive delirium. Of the 566 patients, 184 were randomly assigned to receive placebo, 192 to receive haloperidol, and 190 to receive ziprasidone. The median duration of exposure to a trial drug or placebo was 4 days (interquartile range, 3 to 7). The median number of days alive without delirium or coma was 8.5 (95% confidence interval [CI], 5.6 to 9.9) in the placebo group, 7.9 (95% CI, 4.4 to 9.6) in the haloperidol group, and 8.7 (95% CI, 5.9 to 10.0) in the ziprasidone group (P=0.26 for overall effect across trial groups). The use of haloperidol or ziprasidone, as compared with placebo, had no significant effect on the primary end point (odds ratios, 0.88 [95% CI, 0.64 to 1.21] and 1.04 [95% CI, 0.73 to 1.48], respectively). There were no significant between-group differences with respect to the secondary end points or the frequency of extrapyramidal symptoms. CONCLUSIONS: The use of haloperidol or ziprasidone, as compared with placebo, in patients with acute respiratory failure or shock and hypoactive or hyperactive delirium in the ICU did not significantly alter the duration of delirium. (Funded by the National Institutes of Health and the VA Geriatric Research Education and Clinical Center; MIND-USA ClinicalTrials.gov number, NCT01211522 .)

A solution to the 4-tachyon off-shell amplitude in cubic string field theory

We derive an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a solution we compute the exact coefficient of the quartic effective action relevant for time dependent solutions and we derive the exact coefficient of the quartic tachyon coupling. The rolling tachyon solution expressed as a series of exponentials $e^t$ is studied both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level truncated coefficients are shown to converge to those derived using the exact string amplitude. The agreement with previous work on the subject, both on the quartic tachyon coupling and on the CSFT rolling tachyon, is an excellent test for the accuracy of our off-shell solution.Comment: 26 pages, 5 figure

Casimir Energies for 6D Supergravities Compactified on T_2/Z_N with Wilson Lines

We compute (as functions of the shape and Wilson-line moduli) the one-loop Casimir energy induced by higher-dimensional supergravities compactified from 6D to 4D on 2-tori, and on some of their Z_N orbifolds. Detailed calculations are given for a 6D scalar field having an arbitrary 6D mass m, and we show how to extend these results to higher-spin fields for supersymmetric 6D theories. Particular attention is paid to regularization issues and to the identification of the divergences of the potential, as well as the dependence of the result on m, including limits for which m^2 A> 1 where A is the volume of the internal 2 dimensions. Our calculation extends those in the literature to very general boundary conditions for fields about the various cycles of these geometries. The results have potential applications towards Supersymmetric Large Extra Dimensions (SLED) as a theory of the Dark Energy. First, they provide an explicit calculation within which to follow the dependence of the result on the mass of the bulk states which travel within the loop, and for heavy masses these results bear out the more general analysis of the UV-sensitivity obtained using heat-kernel methods. Second, because the potentials we find describe the dynamics of the classical flat directions of these compactifications, within SLED they would describe the present-day dynamics of the Dark Energy.Comment: 40 pages, 7 figure

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

One-Loop Calculations for a Translation Invariant Non-Commutative Gauge Model

In this paper we discuss one-loop results for the translation invariant non-commutative gauge field model we recently introduced in arXiv:0804.1914. This model relies on the addition of some carefully chosen extra terms in the action which mix long and short scales in order to circumvent the infamous UV/IR mixing, and were motivated by the renormalizable non-commutative scalar model of Gurau et al. (cf. arXiv:0802.0791).Comment: 18 pages, v2: minor correction

Association of germline variation with the survival of women with BRCA1/2 pathogenic variants and breast cancer

Germline genetic variation has been suggested to influence the survival of breast cancer patients independently of tumor pathology. We have studied survival associations of genetic variants in two etiologically unique groups of breast cancer patients, the carriers of germline pathogenic variants in BRCA1 or BRCA2 genes. We found that rs57025206 was significantly associated with the overall survival, predicting higher mortality of BRCA1 carrier patients with estrogen receptor-negative breast cancer, with a hazard ratio 4.37 (95% confidence interval 3.03-6.30, P = 3.1 × 10-9). Multivariable analysis adjusted for tumor characteristics suggested that rs57025206 was an independent survival marker. In addition, our exploratory analyses suggest that the associations between genetic variants and breast cancer patient survival may depend on tumor biological subgroup and clinical patient characteristics

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as