25 research outputs found
Semiclassical strings in Sasaki-Einstein manifolds and long operators in N=1 gauge theories
We study the AdS/CFT relation between an infinite class of 5-d Ypq
Sasaki-Einstein metrics and the corresponding quiver theories. The long BPS
operators of the field theories are matched to massless geodesics in the
geometries, providing a test of AdS/CFT for these cases. Certain small
fluctuations (in the BMN sense) can also be successfully compared. We then go
further and find, using an appropriate limit, a reduced action, first order in
time derivatives, which describes strings with large R-charge. In the field
theory we consider holomorphic operators with large winding numbers around the
quiver and find, interestingly, that, after certain simplifying assumptions,
they can be described effectively as strings moving in a particular metric.
Although not equal, the metric is similar to the one in the bulk. We find it
encouraging that a string picture emerges directly from the field theory and
discuss possible ways to improve the agreement.Comment: 44 pages, LaTeX, 9 figures. v2: References adde
Semiparametric theory and empirical processes in causal inference
In this paper we review important aspects of semiparametric theory and
empirical processes that arise in causal inference problems. We begin with a
brief introduction to the general problem of causal inference, and go on to
discuss estimation and inference for causal effects under semiparametric
models, which allow parts of the data-generating process to be unrestricted if
they are not of particular interest (i.e., nuisance functions). These models
are very useful in causal problems because the outcome process is often complex
and difficult to model, and there may only be information available about the
treatment process (at best). Semiparametric theory gives a framework for
benchmarking efficiency and constructing estimators in such settings. In the
second part of the paper we discuss empirical process theory, which provides
powerful tools for understanding the asymptotic behavior of semiparametric
estimators that depend on flexible nonparametric estimators of nuisance
functions. These tools are crucial for incorporating machine learning and other
modern methods into causal inference analyses. We conclude by examining related
extensions and future directions for work in semiparametric causal inference
Classical/quantum integrability in AdS/CFT
We discuss the AdS/CFT duality from the perspective of integrable systems and
establish a direct relationship between the dimension of single trace local
operators composed of two types of scalar fields in N=4 super Yang-Mills and
the energy of their dual semiclassical string states in AdS(5) X S(5). The
anomalous dimensions can be computed using a set of Bethe equations, which for
``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified
approach to the long wavelength Bethe equations, the classical ferromagnet and
the classical string solutions in the SU(2) sector and present a general
solution, governed by complex curves endowed with meromorphic differentials
with integer periods. Using this solution we compute the anomalous dimensions
of these long operators up to two loops and demonstrate that they agree with
string-theory predictions.Comment: 49 pages, 5 figures, LaTeX; v2: complete proof of the two-loop
equivalence between the sigma model and the gauge theory is added. References
added; v4,v5,v6: misprints correcte
Density Estimation with Replicate Heteroscedastic Measurements
Bandwidth, Bootstrap, Deconvolution, Hypergeometric series, Measurement error,
A Flexible Model for Generalized Linear Regression with Measurement Error
Generalized linear model, Structural model, Surrogate, Validation data, Canonical link, Logistic regression, Mixture distribution, EM algorithm,