Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.Comment: 25 pages, 2 figure

Bergman Kernel from Path Integral

We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kahler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.Comment: 27 page

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.Comment: harvmac, 45 pp. (v2: added references

Stability Walls in Heterotic Theories

We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure

Mucus clearance and lung function in cystic fibrosis with hypertonic saline

BACKGROUND: Abnormal homeostasis of the volume of airway surface liquid in patients with cystic fibrosis is thought to produce defects in mucus clearance and airway defense. Through osmotic forces, hypertonic saline may increase the volume of airway surface liquid, restore mucus clearance, and improve lung function. METHODS: A total of 24 patients with cystic fibrosis were randomly assigned to receive treatment with inhaled hypertonic saline (5 ml of 7 percent sodium chloride) four times daily with or without pretreatment with amiloride. Mucus clearance and lung function were measured during 14-day baseline and treatment periods. RESULTS: Long-term inhalation of hypertonic saline without pretreatment with amiloride (i.e., with placebo pretreatment) resulted in a sustained (≥8 hours) increase in 1-hour rates of mucus clearance, as compared with those with amiloride pretreatment (14.0±2.0 vs. 7.0±1.5 percent, respectively; P = 0.02) and increased 24-hour rates of mucus clearance over baseline. Furthermore, inhalation of hypertonic saline with placebo improved the forced expiratory volume in one second (FEV 1) between the baseline period and the treatment period (mean difference, 6.62 percent; 95 percent confidence interval, 1.6 to 11.7; P = 0.02), whereas hypertonic saline with amiloride did not improve FEV 1 (mean difference, 2.9 percent; 95 percent confidence interval, -2.2 to 8.0; P = 0.23). Forced vital capacity (FVC), the forced expiratory flow between 25 and 75 percent of FVC (FEF 25-75), and respiratory symptoms also significantly improved in patients treated with hypertonic saline and placebo, whereas the residual volume as a proportion of total lung capacity (RV:TLC) did not change in either group. A comparison of the changes in lung function in the two groups showed no significant difference. In vitro data suggested that sustained hydration of airway surfaces was responsible for the sustained improvement in mucus clearance, whereas inhibition of osmotically driven water transport by amiloride accounted for the observed loss of clinical benefit. CONCLUSIONS: In patients with cystic fibrosis, inhalation of hypertonic saline produced a sustained acceleration of mucus clearance and improved lung function. This treatment may protect the lung from insults that reduce mucus clearance and produce lung disease

Monopoles and clusters

We define and study certain hyperkaehler manifolds which capture the asymptotic behaviour of the SU(2)-monopole metric in regions where monopoles break down into monopoles of lower charges. The rate at which these new metrics approximate the monopole metric is exponential, as for the Gibbons-Manton metric.Comment: v2.: relation to calorons mentioned; added explanation

The statistics of string/M theory vacua

We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective Lagrangians, which can be used to precisely study the predictive power of string theory, and in simple examples can lead to universality results. Using these ideas, we outline an approach to estimating the number of vacua of string/M theory which can realize the Standard Model.Comment: harvmac, 72pp (v4: fixed error in discussion of quiver ensembles

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.Comment: 19 pages, late

Stability and duality in N=2 supergravity

The BPS-spectrum is known to change when moduli cross a wall of marginal stability. This paper tests the compatibility of wall-crossing with S-duality and electric-magnetic duality for N=2 supergravity. To this end, the BPS-spectrum of D4-D2-D0 branes is analyzed in the large volume limit of Calabi-Yau moduli space. Partition functions are presented, which capture the stability of BPS-states corresponding to two constituents with primitive charges and supported on very ample divisors in a compact Calabi-Yau. These functions are `mock modular invariant' and therefore confirm S-duality. Furthermore, wall-crossing preserves electric-magnetic duality, but is shown to break the `spectral flow' symmetry of the N=(4,0) CFT, which captures the degrees of freedom of a single constituent.Comment: 25 pages + appendix; v3: final versio