Related papers: Machine Learning Etudes in Conformal Field Theorie…
We develop an approach to construct local bulk operators in a CFT to order $1/N^2$. Since 4-point functions are not fixed by conformal invariance we use the OPE to categorize possible forms for a bulk operator. Using previous results on…
While convolutional neural networks (CNNs) have come to match and exceed human performance in many settings, the tasks these models optimize for are largely constrained to the level of individual objects, such as classification and…
Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful…
Deep neural networks have shown excellent performance in stereo matching task. Recently CNN-based methods have shown that stereo matching can be formulated as a supervised learning task. However, less attention is paid on the fusion of…
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel…
Function plays an important role in mathematics and many science branches. As the fast development of computer technology, more and more study on computational function analysis, e.g., Fast Fourier Transform, Wavelet Transform, Curve…
We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a…
Convolutional Neural Networks (CNNs) have demonstrated state-of-the-art performance on many visual recognition tasks. However, the combination of convolution and pooling operations only shows invariance to small local location changes in…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
The free Maxwell theory in D<>4 dimensions provides a physical example of a unitary, scale invariant theory which is NOT conformally invariant. The easiest way to see this is that the field strength operator F_mn is neither a primary nor a…
Using polarization spinor methods in conjunction with the superspace formalism, we construct 3-point superconformal invariants that are used to determine the form of 3-point correlators of spinning superfield operators in $\mathcal{N}=1$…
Through coarse-graining, tensor network representations of a two-dimensional critical lattice model flow to a universal four-leg tensor, corresponding to a conformal field theory (CFT) fixed-point. We computed explicit elements of the…
We show that the correlator of three large charge operators with minimal scaling dimension can be computed semiclassically in CFTs with a $U(1)$ symmetry for arbitrary fixed values of the ratios of their charges. We obtain explicitly the…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the `eikonalization'…
Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser…
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…