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Related papers: Fast Conformal Bootstrap and Constraints on 3d Gra…

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We initiate the analytical functional bootstrap study of conformal field theories with large $N$ limits. In this first paper we particularly focus on the 1D $O(N)$ vector bootstrap. We obtain a remarkably simple bootstrap equation from the…

High Energy Physics - Theory · Physics 2023-08-09 Zhijin Li

In this long overdue second installment, we continue to develop the conformal bootstrap program for ${\mathcal N}=4$ superconformal field theories in four dimensions via an analysis of the correlation function of four stress-tensor…

High Energy Physics - Theory · Physics 2019-07-24 Christopher Beem , Leonardo Rastelli , Balt C. van Rees

We introduce an approach to find approximate numerical solutions of truncated bootstrap equations for Conformal Field Theories (CFTs) in arbitrary dimensions. The method is based on a stochastic search via a Metropolis algorithm guided by…

High Energy Physics - Theory · Physics 2022-08-17 Alessandro Laio , Uriel Luviano Valenzuela , Marco Serone

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…

High Energy Physics - Theory · Physics 2014-12-05 Sheer El-Showk , Miguel F. Paulos , David Poland , Slava Rychkov , David Simmons-Duffin , Alessandro Vichi

Any unitary compact two-dimensional CFT with $c>1$ and no symmetries beyond Virasoro has a parametrically large density of primary states at large spin for $\bar{h}>\bar{h}_\text{extr}\sim \frac{c-1}{24}$, of a universal form determined by…

High Energy Physics - Theory · Physics 2020-01-29 Henry Maxfield

We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing…

High Energy Physics - Theory · Physics 2017-03-20 David Simmons-Duffin

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…

High Energy Physics - Theory · Physics 2015-10-13 S. El-Showk , M. Paulos , D. Poland , S. Rychkov , D. Simmons-Duffin , A. Vichi

For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to…

High Energy Physics - Theory · Physics 2018-01-17 Jiaxin Qiao , Slava Rychkov

We study two-dimensional (4,4) superconformal field theories of central charge c=6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the…

High Energy Physics - Theory · Physics 2015-11-13 Ying-Hsuan Lin , Shu-Heng Shao , David Simmons-Duffin , Yifan Wang , Xi Yin

We study four-dimensional conformal field theories (CFTs) with an abelian $U(1)$ global symmetry using the conformal bootstrap approach. We obtain numerical bounds on the scaling dimensions of low-lying operators, the stress-tensor central…

High Energy Physics - Theory · Physics 2025-12-25 Denis Karateev , Petr Kravchuk , Andrea Manenti , Marten Reehorst , Alessandro Vichi

Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…

High Energy Physics - Theory · Physics 2017-05-18 Christoph A. Keller , Gregoire Mathys , Ida G. Zadeh

We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$…

High Energy Physics - Theory · Physics 2021-06-08 Chi-Ming Chang , Martin Fluder , Ying-Hsuan Lin , Shu-Heng Shao , Yifan Wang

We initiate the bootstrap program for $\mathcal{N}=3$ superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a $2d$ chiral algebra, and crossing symmetry for…

High Energy Physics - Theory · Physics 2017-04-26 Madalena Lemos , Pedro Liendo , Carlo Meneghelli , Vladimir Mitev

The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…

Statistical Mechanics · Physics 2017-02-01 Hirohiko Shimada , Shinobu Hikami

We propose a roadmap for bootstrapping conformal field theories (CFTs) described by gauge theories in dimensions $d>2$. In particular, we provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap…

High Energy Physics - Theory · Physics 2021-12-29 Yin-Chen He , Junchen Rong , Ning Su

This paper focuses on the analysis of $4d$ $\mathcal{N}=4$ superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is…

High Energy Physics - Theory · Physics 2017-03-08 Pedro Liendo , Carlo Meneghelli

We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We…

High Energy Physics - Theory · Physics 2014-12-05 Filip Kos , David Poland , David Simmons-Duffin

We study the tricritical Ising universality class using conformal bootstrap techniques. By studying bootstrap constraints originating from multiple correlators on the CFT data of multiple OPEs, we are able to determine the scaling dimension…

High Energy Physics - Theory · Physics 2021-05-11 Chethan N Gowdigere , Jagannath Santara , Sumedha

We study the holography of the new conformal higher spin theories imposing general boundary conditions and the near horizon boundary conditions. General boundary conditions lead to the asymptotic symmetry algebra which is a loop algebra of…

High Energy Physics - Theory · Physics 2025-05-14 I. Lovrekovic

We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator…

High Energy Physics - Theory · Physics 2026-03-20 Li-Yuan Chiang , David Poland , Gordon Rogelberg