Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open string invariants in the spirit of Katz-Liu, defining them by localization. The orbifold is viewed as an open chart of a global quotient of the resolved conifold, and the Lagrangian as the fixed locus of an appropriate anti-holomorphic involution. We consider two main applications of the formalism. After warming up with the simpler example of [C^3/Z_3], where we verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main object of our study is the richer case of [C^3/Z_4], where two different choices are allowed for the Lagrangian. For one choice, we make numerical checks to confirm the B-model predictions; for the other, we prove a mirror theorem for orbifold disc invariants, match a large number of annulus invariants, and give mirror symmetry predictions for open string invariants of genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected, version to appear on Selecta Mathematica; v3: last minute mistake found and fixed for the symmetric brane setup of [C^3/Z_4]; in pres

Randomised controlled trial of specialist nurse intervention in heart failure

<p>Objectives. To determine whether specialist nurse intervention improves outcome in patients with chronic heart failure.</p> <p>Design. Randomised controlled trial.</p> <p>Setting. Acute medical admissions unit in a teaching hospital.</p> <p>Participants. 165 patients admitted with heart failure due to left ventricular systolic dysfunction. The intervention started before discharge and continued thereafter with home visits for up to 1 year.</p> <p>Main outcome measures. Time to first event analysis of death from all causes or readmission to hospital with worsening heart failure.</p> <p>Results. 31 patients (37%) in the intervention group died or were readmitted with heart failure compared with 45 (53%) in the usual care group (hazard ratio=0.61, 95% confidence interval 0.33 to 0.96).Compared with usual care, patients in the intervention group had fewer readmissions for any reason (86 v 114, P=0.018), fewer admissions for heart failure (19 v 45, P<0.001) and spent fewer days in hospital for heart failure (mean 3.43 v 7.46 days, P=0.0051).</p> <p>Conclusions. Specially trained nurses can improve the outcome of patients admitted to hospital with heart failure.</p&gt

Closed string tachyons, flips and conifolds

Following the analysis of tachyons and orbifold flips described in hep-th/0412337, we study nonsupersymmetric analogs of the supersymmetric conifold singularity and show using their toric geometry description that they are nonsupersymmetric orbifolds of the latter. Using linear sigma models, we see that these are unstable to localized closed string tachyon condensation and exhibit flip transitions between their two small resolutions (involving 2-cycles), in the process mediating mild dynamical topology change. Our analysis shows that the structure of these nonsupersymmetric conifolds as quotients of the supersymmetric conifold obstructs the 3-cycle deformation of such singularities, suggesting that these nonsupersymmetric conifolds decay by evolving towards their stable small resolutions.Comment: Latex, 22 pgs, 2 figs. v4: matches JHEP version, 29 pgs, 3 figures, more elaborate Introduction, various clarifications adde

Penrose Limits of Orbifolds and Orientifolds

We study the Penrose limit of various AdS_p X S^q orbifolds. The limiting spaces are waves with parallel rays and singular wave fronts. In particular, we consider the orbifolds AdS_3 X S^3/\Gamma, AdS_5 X S^5/\Gamma and AdS_{4,7} X S^{7,4}/\Gamma where \Gamma acts on the sphere and/or the AdS factor. In the pp-wave limit, the wave fronts are the orbifolds C^2/\Gamma, C^4/\Gamma and R XC^4/\Gamma, respectively. When desingularization is possible, we get asymptotically locally pp-wave backgrounds (ALpp). The Penrose limit of orientifolds are also discussed. In the AdS_5 X RP^5 case, the limiting singularity can be resolved by an Eguchi-Hanson gravitational instanton. The pp-wave limit of D3-branes near singularities in F-theory is also presented. Finally, we give the embedding of D-dimensional pp-waves in flat M^{2,D} space.Comment: 20 pages, references adde

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi--Yau $d$-folds are somewhat different from the ``special K\"ahler manifolds'' which had occurred for $d=3$, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi--Yau manifolds. Our results agree with those obtained by more traditional mathematical methods in the limited number of cases for which the latter analysis can be carried out. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.Comment: 44 pages plus 3 tables using harvma

Perturbative Gauge Theory and Closed String Tachyons

We find an interesting connection between perturbative large N gauge theory and closed superstrings. The gauge theory in question is found on N D3-branes placed at the tip of the cone R^6/Gamma. In our previous work we showed that, when the orbifold group Gamma breaks all supersymmetry, then typically the gauge theory is not conformal because of double-trace couplings whose one-loop beta functions do not possess real zeros. In this paper we observe a precise correspondence between the instabilities caused by the flow of these double-trace couplings and the presence of tachyons in the twisted sectors of type IIB theory on orbifolds R^{3,1}x R^6/Gamma. For each twisted sectors that does not contain tachyons, we show that the corresponding double-trace coupling flows to a fixed point and does not cause an instability. However, whenever a twisted sector is tachyonic, we find that the corresponding one-loop beta function does not have a real zero, hence an instability is likely to exist in the gauge theory. We demonstrate explicitly the one-to-one correspondence between the regions of stability/instability in the space of charges under Gamma that arise in the perturbative gauge theory and in the free string theory. Possible implications of this remarkably simple gauge/string correspondence are discussed.Comment: 25 pages, Latex; V2: Clarifications and references adde

Toda systems in closed string tachyon condensation

We consider $tt^*$ equations appearing in the study of localized tachyon condensations. They are described by various Toda system when we consider the condensation by the lowest tachyon corresponding to the monomial $xy$. The tachyon potential is calculated as a solution to these equations. The Toda system appearing in the deformation of \C^2/\Z_n by $xy$ is identical to that of $D_n$ singularity deformed by $x$. For \C^3/\Z_n with $xyz$ deformation, we find only generic non-simple form, similar to the case appearing in \C/\Z_5\to \C/\Z_3 and we discuss the difficulties in these cases.Comment: 20 pages, no figur

From E_8 to F via T

We argue that T-duality and F-theory appear automatically in the E_8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E_8 bundle. If we compactify on a two-torus, this data specifies an LLE_8 bundle where LG is a centrally-extended loopgroup of G. If one of the circles of the torus is smaller than sqrt(alpha') then it is also smaller than a nontrivial circle S in the LLE_8 fiber and so a dimensional reduction on the total space of the bundle is not valid. We conjecture that S is the circle on which the T-dual type IIB theory is compactified, with the aforementioned torus playing the role of the F-theory torus. As tests we reproduce the T-dualities between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find the desired F-theory monodromy. Using Hull's proposal for massive IIA, this realization of T-duality allows us to confirm that the Romans mass is the central extension of our LE_8. In addition this construction immediately reproduces the conjectured formula for global topology change from T-duality with H-flux.Comment: 25 pages, 4 eps figure

Mastering the Master Space

Supersymmetric gauge theories have an important but perhaps under-appreciated notion of a master space, which controls the full moduli space. For world-volume theories of D-branes probing a Calabi-Yau singularity X the situation is particularly illustrative. In the case of one physical brane, the master space F is the space of F-terms and a particular quotient thereof is X itself. We study various properties of F which encode such physical quantities as Higgsing, BPS spectra, hidden global symmetries, etc. Using the plethystic program we also discuss what happens at higher number N of branes. This letter is a summary and some extensions of the key points of a longer companion paper arXiv:0801.1585.Comment: 10 pages, 1 Figur

The Elliptic curves in gauge theory, string theory, and cohomology

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, thes elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various generalized cohomology theories, including elliptic cohomology, and we note that the above two seemingly unrelated descriptions can be unified using Sen's picture of the orientifold limit of F-theory compactification on K3, which unifies the Seiberg-Witten curve with the F-theory curve, and through which we naturally explain the constancy of the modulus that emerges from elliptic cohomology. This also clarifies the orbifolding performed in the previous work and justifies the appearance of the w_4 condition in the elliptic refinement of the mod 2 part of the partition function. We comment on the cohomology theory needed for the case when the modular parameter varies in the base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification