496 research outputs found
Aspects of Collapsing Cycles
Much has been learned about string theory over the last few years by studying
properties of cycles and branes in a given background geometry. Here we discuss
three situations (quantum volume, attractor flows/D-brane stability, and
dynamical topology change) in which cycles in a Calabi-Yau background evolve
and/or degenerate in some manner, yielding various insights into aspects of
quantum geometry. Based in part on talk given at Strings 2000.Comment: 13 pages, 8 figures, Late
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
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
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>
Quantum Deconstruction of a 5D SYM and its Moduli Space
We deconstruct the fifth dimension of the 5D SYM theory with SU(M) gauge
symmetry and Chern-Simons level k=M and show how the 5D moduli space follows
from the non-perturbative analysis of the 4D quiver theory. The 5D coupling
h=1/(g_5)^2 of the un-broken SU(M) is allowed to take any non-negative values,
but it cannot be continued to h<0 and there are no transitions to other phases
of the theory. The alternative UV completions of the same 5D SYM -- via M
theory on the C^3/Z_2M orbifold or via the dual five-brane web in type IIB
string theory -- have identical moduli spaces: h >= 0 only, and no flop
transitions. We claim these are intrinsic properties of the SU(M) SYM theory
with k=M.Comment: 46 Page
Geometric Singularities and Enhanced Gauge Symmetries
Using ``Tate's algorithm,'' we identify loci in the moduli of F-theory
compactifications corresponding to enhanced gauge symmetry. We apply this to
test the proposed F-theory/heterotic dualities in six dimensions. We recover
the perturbative gauge symmetry enhancements of the heterotic side and the
physics of small instantons, and discover new mixed
perturbative/non-perturbative gauge symmetry enhancements. Upon further
toroidal compactification to 4 dimensions, we derive the chain of Calabi-Yau
threefolds dual to various Coulomb branches of heterotic strings.Comment: 49 pages harvmac big (must print in big mode for tables to appear
correctly); Typos and reference correcte
Virtual Structure Constants as Intersection Numbers of Moduli Space of Polynomial Maps with Two Marked Points
In this paper, we derive the virtual structure constants used in mirror
computation of degree k hypersurface in CP^{N-1}, by using localization
computation applied to moduli space of polynomial maps from CP^{1} to CP^{N-1}
with two marked points. We also apply this technique to non-nef local geometry
O(1)+O(-3)->CP^{1} and realize mirror computation without using Birkhoff
factorization.Comment: 10 pages, latex, a minor change in Section 4, English is refined,
Some typing errors in Section 3 are correcte
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 -folds are somewhat different from the ``special K\"ahler
manifolds'' which had occurred for , 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
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