Related papers: Finite-$N$ Bootstrap Constraints in Matrix and Ten…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
We consider a matrix model with d matrices NxN and show that in the limit of large N and d=0 the model describes the knot diagrams. The same limit in matrix string theory is also discussed. We speculate that a prototypical M(atrix) without…
Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…
We study the conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N) singlet and symmetric tensor operators appearing in the $\phi_i \times \phi_j$ OPE, where…
We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the…
We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization.…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values…
Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
The contraction of tensor networks is a central task in the application of tensor network methods to the study of quantum and classical many body systems. In this paper, we investigate the impact of gauge degrees of freedom in the virtual…
In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases…
We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We derive one-point functions of the loop operators of Hermitian matrix-chain models at finite $N$ in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
We show that $\N=1$ gauge theories with an adjoint chiral multiplet admit a wide class of large-N double-scaling limits where $N$ is taken to infinity in a way coordinated with a tuning of the bare superpotential. The tuning is such that…
We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for…
We consider the 2D S-matrix bootstrap in the presence of supersymmetry, $\mathbb{Z}_2$ and $\mathbb{Z}_4$ symmetry. At the boundary of the allowed S-matrix space we encounter well known integrable models such as the supersymmetric…
Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…