146 research outputs found
Direct Integration and Non-Perturbative Effects in Matrix Models
We show how direct integration can be used to solve the closed amplitudes of
multi-cut matrix models with polynomial potentials. In the case of the cubic
matrix model, we give explicit expressions for the ring of non-holomorphic
modular objects that are needed to express all closed matrix model amplitudes.
This allows us to integrate the holomorphic anomaly equation up to holomorphic
modular terms that we fix by the gap condition up to genus four. There is an
one-dimensional submanifold of the moduli space in which the spectral curve
becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic
modular ring of the group . On that submanifold, the gap conditions
completely fix the holomorphic ambiguity and the model can be solved explicitly
to very high genus. We use these results to make precision tests of the
connection between the large order behavior of the 1/N expansion and
non-perturbative effects due to instantons. Finally, we argue that a full
understanding of the large genus asymptotics in the multi-cut case requires a
new class of non-perturbative sectors in the matrix model.Comment: 51 pages, 8 figure
Konishi anomaly approach to gravitational F-terms
We study gravitational corrections to the effective superpotential in
theories with a single adjoint chiral multiplet, using the generalized Konishi
anomaly and the gravitationally deformed chiral ring. We show that the genus
one correction to the loop equation in the corresponding matrix model agrees
with the gravitational corrected anomaly equations in the gauge theory. An
important ingrediant in the proof is the lack of factorization of chiral gauge
invariant operators in presence of a supergravity background. We also find a
genus zero gravitational correction to the superpotential, which can be removed
by a field redefinition.Comment: 28 pages, uses JHEP3.cl
Open/Closed String Duality for Topological Gravity with Matter
The exact FZZT brane partition function for topological gravity with matter
is computed using the dual two-matrix model. We show how the effective theory
of open strings on a stack of FZZT branes is described by the generalized
Kontsevich matrix integral, extending the earlier result for pure topological
gravity. Using the well-known relation between the Kontsevich integral and a
certain shift in the closed-string background, we conclude that these models
exhibit open/closed string duality explicitly. Just as in pure topological
gravity, the unphysical sheets of the classical FZZT moduli space are
eliminated in the exact answer. Instead, they contribute small, nonperturbative
corrections to the exact answer through Stokes' phenomenon.Comment: 23 pages, 1 figure, harvma
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
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
We develop techniques to compute multi-instanton corrections to the 1/N
expansion in matrix models described by orthogonal polynomials. These
techniques are based on finding trans-series solutions, i.e. formal solutions
with exponentially small corrections, to the recursion relations characterizing
the free energy. We illustrate this method in the Hermitian, quartic matrix
model, and we provide a detailed description of the instanton corrections in
the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel
resummation techniques and results from the theory of resurgent functions to
relate the formal multi-instanton series to the nonperturbative definition of
the matrix model. We study this relation in the case of the GWW model and its
double-scaling limit, providing in this way a nice illustration of various
mechanisms connecting the resummation of perturbative series to nonperturbative
results, like the cancellation of nonperturbative ambiguities. Finally, we
argue that trans-series solutions are also relevant in the context of
topological string theory. In particular, we point out that in topological
string models with both a matrix model and a large N gauge theory description,
the nonperturbative, holographic definition involves a sum over the
multi-instanton sectors of the matrix modelComment: 50 pages, 12 figures, comments and references added, small
correction
Nonperturbative aspects of ABJM theory
Using the matrix model which calculates the exact free energy of ABJM theory
on S^3 we study non-perturbative effects in the large N expansion of this
model, i.e., in the genus expansion of type IIA string theory on AdS4xCP^3. We
propose a general prescription to extract spacetime instanton actions from
general matrix models, in terms of period integrals of the spectral curve, and
we use it to determine them explicitly in the ABJM matrix model, as exact
functions of the 't Hooft coupling. We confirm numerically that these
instantons control the asymptotic growth of the genus expansion. Furthermore,
we find that the dominant instanton action at strong coupling determined in
this way exactly matches the action of an Euclidean D2-brane instanton wrapping
RP^3.Comment: 26 pages, 14 figures. v2: small corrections, final version published
in JHE
Syncretism or correlation: Teilhard and Tillich's contrasting methodological approaches to science and theology
This is the pre-peer reviewed version of the article, published in Zygon 40(3) pp.739-750, which has been published in final form at http://www3.interscience.wiley.com/journal/118699350/issueThis paper revisits Paul Tillich’s theological methodology, and contrasts his practice of correlation with the syncretistic methodological practices of Teilhard de Chardin. I argue that the method of correlation, as referred to in Robert John Russell’s 2001 Zygon article, fails to uphold Tillich’s self-limitation of his own methodology with regard to Tillich’s insistence upon the theological circle. I assert that the theological circle, as taken from Systematic Theology I, is a central facet within Tillich’s methodology and that this often ignored concept needs to be resuscitated if one is to remain authentically Tillichian in one’s approach to the science and theology dialogue
A new twist on dS/CFT
We stress that the dS/CFT correspondence should be formulated using unitary
principal series representations of the de Sitter isometry group/conformal
group, rather than highest-weight representations as originally proposed. These
representations, however, are infinite-dimensional, and so do not account for
the finite gravitational entropy of de Sitter space in a natural way. We then
propose to replace the classical isometry group by a q-deformed version. This
is carried out in detail for two-dimensional de Sitter and we find that the
unitary principal series representations deform to finite-dimensional unitary
representations of the quantum group. We believe this provides a promising
microscopic framework to account for the Bekenstein-Hawking entropy of de
Sitter space.Comment: 21 pages, revtex, v2 references adde
Transcriptomics and adaptive genomics of the asymptomatic bacteriuria Escherichia coli strain 83972
Escherichia coli strains are the major cause of urinary tract infections in humans. Such strains can be divided into virulent, UPEC strains causing symptomatic infections, and asymptomatic, commensal-like strains causing asymptomatic bacteriuria, ABU. The best-characterized ABU strain is strain 83972. Global gene expression profiling of strain 83972 has been carried out under seven different sets of environmental conditions ranging from laboratory minimal medium to human bladders. The data reveal highly specific gene expression responses to different conditions. A number of potential fitness factors for the human urinary tract could be identified. Also, presence/absence data of the gene expression was used as an adaptive genomics tool to model the gene pool of 83972 using primarily UPEC strain CFT073 as a scaffold. In our analysis, 96% of the transcripts filtered present in strain 83972 can be found in CFT073, and genes on six of the seven pathogenicity islands were expressed in 83972. Despite the very different patient symptom profiles, the two strains seem to be very similar. Genes expressed in CFT073 but not in 83972 were identified and can be considered as virulence factor candidates. Strain 83972 is a deconstructed pathogen rather than a commensal strain that has acquired fitness properties
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