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Related papers: Bootstrapping the O(N) Vector Models

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We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm,…

High Energy Physics - Theory · Physics 2014-07-31 David Poland , David Simmons-Duffin , Alessandro Vichi

We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension \Delta of the leading scalar operator…

High Energy Physics - Theory · Physics 2015-03-13 Vyacheslav S. Rychkov , Alessandro Vichi

We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension…

High Energy Physics - Theory · Physics 2016-01-20 Apratim Kaviraj , Kallol Sen , Aninda Sinha

We implement the conformal bootstrap for N=4 superconformal field theories in four dimensions. Consistency of the four-point function of the stress-energy tensor multiplet imposes significant upper bounds for the scaling dimensions of…

High Energy Physics - Theory · Physics 2022-08-22 Christopher Beem , Leonardo Rastelli , Balt C. van Rees

We study behaviour of the critical $O(N)$ vector model with quartic interaction in $2 \leq d \leq 6$ dimensions to the next-to-leading order in the large-$N$ expansion. We derive and perform consistency checks that provide an evidence for…

High Energy Physics - Theory · Physics 2020-07-15 Mikhail Goykhman , Michael Smolkin

Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…

High Energy Physics - Theory · Physics 2023-07-12 Ying-Hsuan Lin , Shu-Heng Shao

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

Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries…

Strongly Correlated Electrons · Physics 2026-04-24 Jiechao Feng , Taige Wang

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can…

High Energy Physics - Theory · Physics 2021-03-29 Zhijin Li , David Poland

We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of…

High Energy Physics - Theory · Physics 2026-02-17 Rajeev S. Erramilli , Matthew S. Mitchell

Using Operator Product Expansions and a graphical ansatz for the four-point function of the fundamental field \phi^{\alpha}(x) in the conformally invariant O(N) vector model, we calculate the next-to-leading order in 1/N values of the…

High Energy Physics - Theory · Physics 2009-10-28 A. C. Petkou

The four point function of Conformal Field Theories (CFT's) with global symmetry gives rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental…

High Energy Physics - Theory · Physics 2015-05-28 Alessandro Vichi

The Euclidean Anti-de Sitter (AdS) space provides a natural framework for studying boundary conformal field theory (BCFT). We analyze the conformal boundary conditions of the critical O$(N)$ model in $d=4-\epsilon$ dimensions using the…

High Energy Physics - Theory · Physics 2025-07-31 Simone Giombi , Zimo Sun

Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with…

High Energy Physics - Theory · Physics 2020-11-23 Andreas Stergiou

We study the critical properties of scalar field theories in $d+1$ dimensions with $O(N)$ invariant interactions localized on a $d$-dimensional boundary. By a combination of large $N$ and epsilon expansions, we provide evidence for the…

High Energy Physics - Theory · Physics 2020-09-29 Simone Giombi , Himanshu Khanchandani

We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the…

High Energy Physics - Theory · Physics 2024-05-31 Stefanos R. Kousvos , Alessandro Piazza , Alessandro Vichi

This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c > 2$ such that for $2…

Statistical Mechanics · Physics 2022-06-15 Jaychandran Padayasi , Abijith Krishnan , Max A. Metlitski , Ilya A. Gruzberg , Marco Meineri

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…

High Energy Physics - Theory · Physics 2018-10-17 Junchen Rong , Ning Su

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

We explore constraints on (1+1)$d$ unitary conformal field theory with an internal $\mathbb{Z}_N$ global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints…

High Energy Physics - Theory · Physics 2021-06-09 Ying-Hsuan Lin , Shu-Heng Shao