Related papers: A functional approach to the numerical conformal b…
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 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 introduce a new approach to the study of the crossing equation for CFTs in the presence of a boundary. We argue that there is a basis for this equation related to the generalized free field solution. The dual basis is a set of linear…
The crossing equations of a conformal field theory can be systematically truncated to a finite, closed system of polynomial equations. In certain cases, solutions of the truncated equations place strict bounds on the space of all unitary…
We study a general class of functionals providing an analytic handle on the conformal bootstrap equations in one dimension. We explicitly identify the extremal functionals, corresponding to theories saturating conformal bootstrap bounds, in…
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 propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new approach, we reverse the…
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…
In this letter we study how the exact non-perturbative integrability methods in 4D N=4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access…
We provide an effective solution of the 1D crossing equation. We begin by arguing that crossing constraints can be recast in terms of bases of sum rules associated to special sets of CFT data -- extremal solutions -- which solve these…
We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE,…
The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may…
We introduce a novel method to bootstrap crossing equations in Conformal Field Theory and apply it to finite temperature theories on $S^1\times \mathbb{R}^{d-1}$. The proposed approach does not rely on positivity constraints and does not…
We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal…
In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft…
We propose a bootstrap program for CFTs near intersecting boundaries which form a co-dimension 2 edge. We describe the kinematical setup and show that bulk 1-pt functions and bulk-edge 2-pt functions depend on a non-trivial cross-ratio and…
Adjoint methods have gained popularity in recent years for driving adaptation procedures which aim to reduce error in solution functionals. While adjoint methods have been proven effective for functional-based adaptation, the practical…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals…
Recently an efficient numerical method has been developed to implement the constraints of crossing symmetry and unitarity on the operator dimensions and OPE coefficients of conformal field theories (CFT) in diverse space-time dimensions. It…