Localized Tachyons and the Quantum McKay Correspondence

The condensation of closed string tachyons localized at the fixed point of a C^d/\Gamma orbifold can be studied in the framework of renormalization group flow in a gauged linear sigma model. The evolution of the Higgs branch along the flow describes a resolution of singularities via the process of tachyon condensation. The study of the fate of D-branes in this process has lead to a notion of a ``quantum McKay correspondence.'' This is a hypothetical correspondence between fractional branes in an orbifold singularity in the ultraviolet with the Coulomb and Higgs branch branes in the infrared. In this paper we present some nontrivial evidence for this correspondence in the case C^2/Z_n by relating the intersection form of fractional branes to that of ``Higgs branch branes,'' the latter being branes which wrap nontrivial cycles in the resolved space.Comment: 25 pages; harvma

Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories

We study (p,q)=(2,4k) minimal superstrings within the minimal superstring field theory constructed in hep-th/0611045. We explicitly give a solution to the W_{1+\infty} constraints by using charged D-instanton operators, and show that the (m,n)-instanton sector with m positive-charged and n negative-charged ZZ-branes is described by an (m+n)\times (m+n) supermatrix model. We argue that the supermatrix model can be regarded as an open string field theory on the multi ZZ-brane system.Comment: 15 pages, 1 figure, minor chang

Notes on the algebraic curves in (p,q) minimal string theory

Loop amplitudes in (p,q) minimal string theory are studied in terms of the continuum string field theory based on the free fermion realization of the KP hierarchy. We derive the Schwinger-Dyson equations for FZZT disk amplitudes directly from the W_{1+\infty} constraints in the string field formulation and give explicitly the algebraic curves of disk amplitudes for general backgrounds. We further give annulus amplitudes of FZZT-FZZT, FZZT-ZZ and ZZ-ZZ branes, generalizing our previous D-instanton calculus from the minimal unitary series (p,p+1) to general (p,q) series. We also give a detailed explanation on the equivalence between the Douglas equation and the string field theory based on the KP hierarchy under the W_{1+\infty} constraints.Comment: 61 pages, 1 figure, section 2.5 and Appendix B added, references added, final version to appear in JHE

NS5-Branes, T-Duality and Worldsheet Instantons

The equivalence of NS5-branes and ALF spaces under T-duality is well known. However, a naive application of T-duality transforms the ALF space into a smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper we re-examine this duality, starting from a two-dimensional N=(4,4) gauged linear sigma model describing Taub-NUT space. After dualizing the circle fiber, we find that the smeared NS5-brane target space metric receives corrections from multi-worldsheet instantons. These instantons are identified as Nielsen-Olesen vortices. We show that their effect is to break the isometry of the target space, localizing the NS5-brane at a point. The contribution from the k-instanton sector is shown to be proportional to the weighted integral of the Euler form over the k-vortex moduli space. The duality also predicts the, previously unknown, asymptotic exponential decay coefficient of the BPS vortex solution.Comment: 26 pages. v2: Fourier modes of multi-vortex fermion zero mode corrected. Reference added. v3: typo correcte

Quivers from Matrix Factorizations

We discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity. This method also yields explicit geometrical interpretations of D-branes (i.e., quiver representations) on a resolution given in terms of Grassmannians. As an example we analyze some non-toric singularities which are resolved by a single CP1 but have "length" greater than one. These examples have a much richer structure than conifolds. A picture is proposed that relates matrix factorizations in Landau-Ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions.Comment: 33 pages, (minor changes

Epigenomic profiling of newborns with isolated orofacial clefts reveals widespread DNA methylation changes and implicates metastable epiallele regions in disease risk.

Cleft lip with or without cleft palate (CL/P) is a common human birth defect whose etiologies remain largely unknown. Several studies have demonstrated that periconceptional supplementation of folic acid can reduce risk of CL/P in offspring. In this study, we tested the hypothesis that the preventive effect of folic acid is manifested through epigenetic modifications by determining whether DNA methylation changes are associated with CL/P. To more readily observe the potential effects of maternal folate on the offspring epigenome, we focused on births prior to mandatory dietary folate fortification in the United States (i.e. birth year 1997 or earlier). Genomic DNA methylation levels were assessed from archived newborn bloodspots in a 182-member case-control study using the Illumina® Human Beadchip 450K array. CL/P cases displayed striking epigenome-wide hypomethylation relative to controls: 63% of CpGs interrogated had lower methylation levels in case newborns, a trend which held up in racially stratified sub-groups. 28 CpG sites reached epigenome-wide significance and all were case-hypomethylated. The most significant CL/P-associated differentially methylated region encompassed the VTRNA2-1 gene, which was also hypomethylated in cases (FWER p = 0.014). This region has been previously characterized as a nutritionally-responsive, metastable epiallele and CL/P-associated methylation changes, in general, were greater at or near putative metastable epiallelic regions. Gene Set Enrichment Analysis of CL/P-associated DMRs showed an over-representation of genes involved in palate development such as WNT9B, MIR140 and LHX8. CL/P-associated DNA methylation changes may partly explain the mechanism by which orofacial clefts are responsive to maternal folate levels

The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell \Gr of the Sato Grassmannian $Gr$. This is a consequence of a well-defined continuum limit in which the string equation has the simple form \lb \cp ,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- $2\times 2$ matrices of differential operators. These conditions on $V_1$ and $V_2$ yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate the two modified-KdV \t-functions whose product gives the partition function of the Unitary Matrix Model.Comment: 21 page

Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate the EPs in OQS, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. We also report the precise number of EPs occurring in an OQS with a continuum described by a quadratic dispersion curve. In particular, the number of EPs occurring in a bare discrete Hamiltonian of dimension $n_\textrm{D}$ is given by $n_\textrm{D} (n_\textrm{D} - 1)$; if this discrete Hamiltonian is then coupled to continuum (or continua) to form an OQS, the interaction with the continuum generally produces an enlarged discrete solution space that includes a greater number of EPs, specifically $2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) [2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) - 1]$, in which $n_\textrm{C}$ is the number of (non-degenerate) continua to which the discrete sector is attached. Finally, we offer a heuristic quantum phase transition analogy for the emergence of the resonance (giving rise to irreversibility via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the above eigenvalue expansion.Comment: 16 pages, 7 figure

The origin of fracture in the I-ECAP of AZ31B magnesium alloy

Magnesium alloys are very promising materials for weight-saving structural applications due to their low density, comparing to other metals and alloys currently used. However, they usually suffer from a limited formability at room temperature and low strength. In order to overcome those issues, processes of severe plastic deformation (SPD) can be utilized to improve mechanical properties, but processing parameters need to be selected with care to avoid fracture, very often observed for those alloys during forming. In the current work, the AZ31B magnesium alloy was subjected to SPD by incremental equal-channel angular pressing (I-ECAP) at temperatures varying from 398 K to 525 K (125 °C to 250 °C) to determine the window of allowable processing parameters. The effects of initial grain size and billet rotation scheme on the occurrence of fracture during I-ECAP were investigated. The initial grain size ranged from 1.5 to 40 µm and the I-ECAP routes tested were A, BC, and C. Microstructures of the processed billets were characterized before and after I-ECAP. It was found that a fine-grained and homogenous microstructure was required to avoid fracture at low temperatures. Strain localization arising from a stress relaxation within recrystallized regions, namely twins and fine-grained zones, was shown to be responsible for the generation of microcracks. Based on the I-ECAP experiments and available literature data for ECAP, a power law between the initial grain size and processing conditions, described by a Zener–Hollomon parameter, has been proposed. Finally, processing by various routes at 473 K (200 °C) revealed that route A was less prone to fracture than routes BC and C

Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte