91,395 research outputs found
Worldsheet Properties of Extremal Correlators in AdS/CFT
We continue to investigate planar four point worldsheet correlators of string
theories which are conjectured to be duals of free gauge theories. We focus on
the extremal correlators <Tr(Z^{J_1}(x)) Tr(Z^{J_2}(y)) Tr(Z^{J_3}(z))
Tr(\bar{Z}^{J}(0))> of SYM theory, and construct the corresponding
worldsheet correlators in the limit when the . The worldsheet
correlator gets contributions, in this limit, from a whole family of Feynman
graphs. We find that it is supported on a {\it curve} in the moduli space
parametrised by the worldsheet crossratio. In a further limit of the spacetime
correlators we find this curve to be the unit circle. In this case, we also
check that the entire worldsheet correlator displays the appropriate crossing
symmetry. The non-renormalization of the extremal correlators in the 't Hooft
coupling offers a potential window for a comparison of these results with those
from strong coupling.Comment: 27 pages, 5 figure
Dual quadratic differentials and entire minimal graphs in Heisenberg space
We define holomorphic quadratic differentials for spacelike surfaces with
constant mean curvature in the Lorentzian homogeneous spaces
with isometry group of dimension 4, which are dual to
the Abresch-Rosenberg differentials in the Riemannian counterparts
, and obtain some consequences. On the one hand, we
give a very short proof of the Bernstein problem in Heisenberg space, and
provide a geometric description of the family of entire graphs sharing the same
differential in terms of a 2-parameter conformal deformation. On the other
hand, we prove that entire minimal graphs in Heisenberg space have negative
Gauss curvature.Comment: 19 page
Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models
Motivated by a real-life problem of sharing social network data that contain
sensitive personal information, we propose a novel approach to release and
analyze synthetic graphs in order to protect privacy of individual
relationships captured by the social network while maintaining the validity of
statistical results. A case study using a version of the Enron e-mail corpus
dataset demonstrates the application and usefulness of the proposed techniques
in solving the challenging problem of maintaining privacy \emph{and} supporting
open access to network data to ensure reproducibility of existing studies and
discovering new scientific insights that can be obtained by analyzing such
data. We use a simple yet effective randomized response mechanism to generate
synthetic networks under -edge differential privacy, and then use
likelihood based inference for missing data and Markov chain Monte Carlo
techniques to fit exponential-family random graph models to the generated
synthetic networks.Comment: Updated, 39 page
Feynman integral relations from parametric annihilators
We study shift relations between Feynman integrals via the Mellin transform
through parametric annihilation operators. These contain the momentum space IBP
relations, which are well-known in the physics literature. Applying a result of
Loeser and Sabbah, we conclude that the number of master integrals is computed
by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate
techniques to compute this Euler characteristic in various examples and compare
it with numbers of master integrals obtained in previous works.Comment: v2: new section 3.1 added, several misprints corrected and additional
remark
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