Related papers: Universal Correlators from Geometry
The existence of abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau fourfold and has important phenomenological consequences. We study conceptual and…
This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the…
Symmetric product orbifolds provide a controlled environment to explore generic features of gauge theory and holography. The tractability of these theories lies in the complete characterisation of their gauge structure through holomorphic…
Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…
As a step towards the classification of supergravity backgrounds with flux, we study the (back-reacted) geometry created by a BPS M2-brane when it wraps a cycle in a Calabi-Yau manifold. If it is to preserve supersymmetry, the membrane…
Using U-duality, the properties of the matrix theories corresponding to the compactification of M-theory on $T^d$ are investigated. The couplings of the $d+1$ dimensional effective Super-Yang-Mills theory to all the M-theory moduli is…
We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…
Neural networks are dynamical systems that compute with their dynamics. One example is the Hopfield model, forming an associative memory which stores patterns as global attractors of the network dynamics. From studies of dynamical networks…
Non-abelian gauge theories in the context of generalized complex geometry are discussed. The generalized connection naturally contains standard gauge and scalar fields, unified in a purely geometric way. We define the corresponding…
Universal enveloping algebras of braided m-Lie algebras and PBW theorem are obtained by means of combinatorics on words.
We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the…
We propose a parameterization for contributions of an infinite set of diagrams (bubble chains) into physical observables represented as integrals of running coupling constant over the finite region in momentum space. The perturbation theory…
We study shallow and deep neural networks whose inputs range over a general topological space. The model is built from a prescribed family of continuous feature maps and reduces to multilayer feedforward networks in the Euclidean case. We…
It has been shown by Strahov and Fyodorov that averages of products and ratios of characteristic polynomials corresponding to Hermitian matrices of a unitary ensemble, involve kernels related to orthogonal polynomials and their Cauchy…
The universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our…
Ever since Yau's non-constructive existence proof of Ricci-flat metrics on Calabi-Yau manifolds, finding their explicit construction remains a major obstacle to development of both string theory and algebraic geometry. Recent computational…
Inner products of neural network feature maps arise in a wide variety of machine learning frameworks as a method of modeling relations between inputs. This work studies the approximation properties of inner products of neural networks. It…
We present a pedagogical introduction to the recent advances in the computational geometry, physical implications, and data science of Calabi-Yau manifolds. Aimed at the beginning research student and using Calabi-Yau spaces as an exciting…
Integral discriminants provide a simple and fundamental model for non-Gaussian integrals, associated with homogeneous polynomials of degree r in n variables. We argue that, in this context, the study of correlators is equally if not more…
We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the…