A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6

We study the moduli space ${\cal M}$ of N=(4,4) superconformal field theories with central charge c=6. After a slight emendation of its global description we find the locations of various known models in the component of ${\cal M}$ associated to K3 surfaces. Among them are the Z_2 and Z_4 orbifold theories obtained from the torus component of ${\cal M}$. Here, SO(4,4) triality is found to play a dominant role. We obtain the B-field values in direction of the exceptional divisors which arise from orbifolding. We prove T-duality for the Z_2 orbifolds and use it to derive the form of ${\cal M}$ purely within conformal field theory. For the Gepner model (2)^4 and some of its orbifolds we find the locations in ${\cal M}$ and prove isomorphisms to nonlinear sigma models. In particular we prove that the Gepner model (2)^4 has a geometric interpretation with Fermat quartic target space.Comment: 58 pages, version submitted to Comm. Math. Phys; references added and minor mistakes correcte

On explicit results at the intersection of the Z_2 and Z_4 orbifold subvarieties in K3 moduli space

We examine the recently found point of intersection between the Z_2 and Z_4 orbifold subvarieties in the K3 moduli space more closely. First we give an explicit identification of the coordinates of the respective Z_2 and Z_4 orbifold theories at this point. Secondly we construct the explicit identification of conformal field theories at this point and show the orthogonality of the two subvarieties.Comment: Latex, 23 page

Symmetry-surfing the moduli space of Kummer K3s.

A maximal subgroup of the Mathieu group M24 arises as the combined holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler class is induced from the underlying complex torus. As a subgroup of M24, this group is the stabilizer group of an octad in the Golay code. To meaningfully combine the symmetry groups of distinct Kummer surfaces, we introduce the concepts of Niemeier markings and overarching maps between pairs of Kummer surfaces. The latter induce a prescription for symmetry-surfing the moduli space, while the former can be seen as a first step towards constructing a vertex algebra that governs the elliptic genus of K3 in an M24-compatible fashion. We thus argue that a geometric approach from K3 to Mathieu Moonshine may bear fruit.Comment: 20 pages; minor changes; accepted for publication in the Proceedings Volume of String-Math 201

Alterations in T1 of normal and reperfused infarcted myocardium after Gd-BOPTA versus GD-DTPA on inversion recovery EPI.

This study tested whether Gd-BOPTA/Dimeg or Gd-DTPA exerts greater relaxation enhancement for blood and reperfused infarcted myocardium. Relaxivity of Gd-BOPTA is increased by weak binding to serum albumin. Thirty-six rats were subjected to reperfused infarction before contrast (doses = 0.05, 0.1, and 0.2 mmol/kg). delta R1 was repeatedly measured over 30 min. Gd-BOPTA caused greater delta R1 for blood and myocardium than did Gd-DTPA; clearance of both agents from normal- and infarcted myocardium was similar to blood clearance; plots of delta R1 myocardium/delta R1 blood showed equilibrium phase contrast distribution. Fractional contrast agent distribution volumes were approximately 0.24 for both agents in normal myocardium, 0.98 and 1.6 for Gd-DTPA and Gd-BOPTA, respectively, in reperfused infarction. The high value for Gd-BOPTPA was ascribed to greater relaxivity in infarction versus blood. It was concluded that Gd-BOPTA/Dimeg causes a greater delta R1 than Gd-DTPA in regions which contain serum albumin

Folding of Hitchin systems and crepant resolutions

Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of ABCDEFG-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of ADE-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi--Yau orbifold stacks constructed by the first author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi--Yau threefolds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems

The ratio of pro- and anti-angiogenic cytokines produced by retinal pigment epithelial cells is shifted to support angiogenesis by complement

Purpose The complement system of age-related macular degeneration (AMD) patients is marginally but chronically over-activated. Retinal pigment epithelial (RPE) cells and photoreceptor cells undergo cell death during the development of this potentially blinding eye disease. In this study the balance between the pro-angiogenic vascular endothelial growth factor (VEGF) and the anti-angiogenic pigment epithelium-derived factor (PEDF) by RPE cells in response to complement serum was analysed. Methods Increasing concentrations of complement competent human serum were incubated with human RPE cells. Controls with the addition of zymosan to activate the complement cascade, zymosan alone, and heat-treated serum with inoperative complement were included. The secretion of VEGF and PEDF was measured by sandwich ELISA. Immunocytochemistry was performed for the in situ detection of VEGF and PEDF. The experiments were supplemented by RT-PCR expression analysis and Western Blot detection of both antagonists. Results Human complement competent serum stimulated the RPE cells to produce enhanced amounts of VEGF while unspecific stimuli showed no influence on the secretion of VEGF. The combination of complement competent serum and zymosan was revealed as the most effective treatment for an increased VEGF production. The PEDF-specific staining of RPE cells decreased with augmented concentrations of complement competent serum. PCR data showed an enhanced amount of VEGF-encoding transcripts and an unaltered or lower amount of PEDF-specific transcripts. Western Blots confirmed the shift in favour of VEGF when compared to PEDF after complement treatment of RPE cells. Conclusions Activated complement may shift the balance between VEGF and PEDF produced by RPE cells towards the blood vessel chemoattractant VEGF. This finding may reveal a mechanism how enhanced complement activation might contribute to a pro-angiogenic retinal environment supporting neovascularisation during the late stage of exsudative AMD

Local RBF approximation for scattered data fitting with bivariate splines

In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given

Numerical Ricci-flat metrics on K3

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2 orbifold with many discrete symmetries. High-resolution metrics may be obtained on a time scale of days using a desktop computer. We compute various geometric and spectral quantities from our numerical metrics. Using similar resources we expect our methods to practically extend to Calabi-Yau three-folds with a high degree of discrete symmetry, although we expect the general three-fold to remain a challenge due to memory requirements.Comment: 38 pages, 10 figures; program code and animations of figures downloadable from http://schwinger.harvard.edu/~wiseman/K3/ ; v2 minor corrections, references adde