3,600 research outputs found
Modular functors, cohomological field theories and topological recursion
Given a topological modular functor in the sense of Walker
\cite{Walker}, we construct vector bundles over ,
whose Chern classes define semi-simple cohomological field theories. This
construction depends on a determination of the logarithm of the eigenvalues of
the Dehn twist and central element actions. We show that the intersection of
the Chern class with the -classes in is
computed by the topological recursion of \cite{EOFg}, for a local spectral
curve that we describe. In particular, we show how the Verlinde formula for the
dimensions is retrieved from the
topological recursion. We analyze the consequences of our result on two
examples: modular functors associated to a finite group (for which
enumerates certain -principle
bundles over a genus surface with boundary conditions specified by
), and the modular functor obtained from Wess-Zumino-Witten
conformal field theory associated to a simple, simply-connected Lie group
(for which is the Verlinde
bundle).Comment: 50 pages, 2 figures. v2: typos corrected and clarification about the
use of ordered pairs of points for glueing. v3: unitarity assumption waived +
discussion of families index interpretation of the correlation functions for
Wess-Zumino-Witten theorie
Open G2 Strings
We consider an open string version of the topological twist previously
proposed for sigma-models with G2 target spaces. We determine the cohomology of
open strings states and relate these to geometric deformations of calibrated
submanifolds and to flat or anti-self-dual connections on such submanifolds. On
associative three-cycles we show that the worldvolume theory is a gauge-fixed
Chern-Simons theory coupled to normal deformations of the cycle. For
coassociative four-cycles we find a functional that extremizes on
anti-self-dual gauge fields. A brane wrapping the whole G2 induces a
seven-dimensional associative Chern-Simons theory on the manifold. This theory
has already been proposed by Donaldson and Thomas as the higher-dimensional
generalization of real Chern-Simons theory. When the G2 manifold has the
structure of a Calabi-Yau times a circle, these theories reduce to a
combination of the open A-model on special Lagrangians and the open
B+\bar{B}-model on holomorphic submanifolds. We also comment on possible
applications of our results.Comment: 55 pages, no figure
Differentiable Rendering for Synthetic Aperture Radar Imagery
There is rising interest in integrating signal and image processing pipelines
into deep learning training to incorporate more domain knowledge. This can lead
to deep neural networks that are trained more robustly and with limited data,
as well as the capability to solve ill-posed inverse problems. In particular,
there is rising interest in differentiable rendering, which allows explicitly
modeling geometric priors and constraints in the optimization pipeline using
first-order methods such as backpropagation. Existing efforts in differentiable
rendering have focused on imagery from electro-optical sensors, particularly
conventional RGB-imagery. In this work, we propose an approach for
differentiable rendering of Synthetic Aperture Radar (SAR) imagery, which
combines methods from 3D computer graphics with neural rendering. We
demonstrate the approach on the inverse graphics problem of 3D Object
Reconstruction from limited SAR imagery using high-fidelity simulated SAR data.Comment: A substantially similar version of this manuscript was submitted to
ECCV 2022 and is under revie
Orbifold Resolution by D-Branes
We study topological properties of the D-brane resolution of
three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups
Gamma. The D-brane vacuum moduli space is shown to fill out the background
spacetime with Fayet--Iliopoulos parameters controlling the size of the
blow-ups. This D-brane vacuum moduli space can be classically described by a
gauged linear sigma model, which is shown to be non-generic in a manner that
projects out non-geometric regions in its phase diagram, as anticipated from a
number of perspectives.Comment: 26 pages, 2 figures (TeX, harvmac big, epsf
Factor Substitution and Factor Augmenting Technical Progress in the US: A Normalized Supply-Side System Approach
Using a normalized CES function with factor-augmenting technical progress, we estimate a supply-side system of the US economy from 1953 to 1998. Avoiding potential estimation biases that have occurred in earlier studies and putting a high emphasis on the consistency of the data set, required by the estimated system, we obtain robust results not only for the aggregate elasticity of substitution but also for the parameters of labor and capital augmenting technical change. We find that the elasticity of substitution is significantly below unity and that the growth rates of technical progress show an asymmetrical pattern where the growth of labor-augmenting technical progress is exponential, while that of capital is hyperbolic or logarithmic.Capital-Labor Substitution, Technological Change, Factor Shares, Normalized CES function, Supply-side system, United States.
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