Related papers: Navigator Function for the Conformal Bootstrap
A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in arXiv:2104.09518. Its efficacy was demonstrated in the simplest example possible, i.e. that of the mixed-correlator study…
We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal…
This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these…
We use the recently developed navigator method to obtain rigorous upper and lower bounds on new OPE data in the 3d Ising CFT. For example, assuming that there are only two $\mathbb{Z}_2$-even scalar operators $\epsilon$ and $\epsilon'$ with…
We study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of "external" parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an optimal point…
We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\bar z$ are sampled. In contrast to the…
We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale…
Navigation functions provide both path and motion planning, which can be used to ensure obstacle avoidance and convergence in the sphere world. When dealing with complex and realistic scenarios, constructing a transformation to the sphere…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible…
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…
In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…
Autonomous exploration is a complex task where the robot moves through an unknown environment with the goal of mapping it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of…
This technical report presents the construction and analysis of polynomial navigation functions for motion planning in 3-D workspaces populated by spherical and cylindrical obstacles. The workspace is modeled as a bounded spherical region,…
This work proposes a novel transformation termed the conformal navigation transformation to achieve collision-free navigation of a robot in a workspace populated with arbitrary polygonal obstacles. The properties of the conformal navigation…
The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite…
We present a low entry-level introduction to the Conformal Bootstrap. We review and obtain several basic bounds using Linear Programming in machine precision in Mathematica, making the results accessible even to the most uneducated computer…
The numerical conformal bootstrap has become in the last 15 years an indispensable tool for studying strongly coupled CFTs in various dimensions. Here we review the main developments in the field in the last 5 years, since the appearance of…
In this work we propose a holistic framework for autonomous aerial inspection tasks, using semantically-aware, yet, computationally efficient planning and mapping algorithms. The system leverages state-of-the-art receding horizon…
This paper brings together the concepts of navigation transformation and harmonic functions to form navigation functions that are correct-by-construction in the sense that no tuning is required. The form of the navigation function is…