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Related papers: Conformal Bootstrap in Mellin Space

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Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…

High Energy Physics - Theory · Physics 2019-04-18 David Poland , Slava Rychkov , Alessandro Vichi

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…

High Energy Physics - Theory · Physics 2021-10-27 António Antunes

We implement the conformal bootstrap program for three-dimensional CFTs with $\mathcal{N}=2$ supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of…

High Energy Physics - Theory · Physics 2015-08-11 Nikolay Bobev , Sheer El-Showk , Dalimil Mazac , Miguel F. Paulos

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

We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $\phi_i$ transforming as an $O(N)$ vector. The crossing symmetry of the…

High Energy Physics - Theory · Physics 2015-05-06 Shai M. Chester , Silviu S. Pufu , Ran Yacoby

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…

High Energy Physics - Theory · Physics 2016-11-04 Alejandro Castedo Echeverri , Benedict von Harling , Marco Serone

We construct a crossing symmetric basis for conformal four-point functions in momentum space by requiring consistent factorization. Just as scattering amplitudes factorize when the intermediate particle is on-shell, non-analytic parts of…

High Energy Physics - Theory · Physics 2018-10-10 Hiroshi Isono , Toshifumi Noumi , Gary Shiu

We study the conformal bootstrap constraints for 3D conformal field theories with a $\mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $\epsilon$ that is invariant under the symmetry. When there is additionally a…

High Energy Physics - Theory · Physics 2018-12-05 Alexander Atanasov , Aaron Hillman , David Poland

We develop an analytic approach to Boundary Conformal Field Theory (BCFT), focussing on the two-point function of a general pair of scalar primary operators. The resulting crossing equation can be thought of as a vector equation in an…

High Energy Physics - Theory · Physics 2020-01-29 Dalimil Mazáč , Leonardo Rastelli , Xinan Zhou

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,…

High Energy Physics - Theory · Physics 2020-05-20 Miguel F. Paulos

We consider holographic CFTs and study their large $N$ expansion. We use Polyakov-Mellin bootstrap to extract the CFT data of all operators, including scalars, till $O(1/N^4)$. We add a contact term in Mellin space, which corresponds to an…

High Energy Physics - Theory · Physics 2020-02-07 Kausik Ghosh

Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…

High Energy Physics - Theory · Physics 2021-02-24 Justin Kaidi , Eric Perlmutter

We provide dramatic evidence that `Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into `left' and `right'…

High Energy Physics - Theory · Physics 2015-03-19 A. Liam Fitzpatrick , Jared Kaplan , Joao Penedones , Suvrat Raju , Balt C. van Rees

Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving…

High Energy Physics - Theory · Physics 2014-12-23 Jin-Beom Bae , Soo-Jong Rey

In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As…

High Energy Physics - Theory · Physics 2016-10-17 Kallol Sen , Aninda Sinha

The Euklidean correlation functions and vacuum expectation values of products of field operators of some Lorentz spin and dimension are expressed through Mellin amplitudes which depend on complex dimensions subject to linear constraints.…

High Energy Physics - Theory · Physics 2009-07-15 Gerhard Mack

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

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…

High Energy Physics - Theory · Physics 2022-02-02 Gergely Kántor , Vasilis Niarchos , Constantinos Papageorgakis

The operator product expansion (OPE) of twist operators in the replica trick framework enables a long-distance expansion of the mutual information (MI) in conformal field theories (CFTs). In this expansion, the terms are labeled by primary…

High Energy Physics - Theory · Physics 2025-09-05 Cesar A. Agon , Horacio Casini , Umut Gürsoy , Guim Planella Planas

We investigate two aspects of conformal field theories. In the first part, we study the general 4-point correlator of identical scalars around the fully crossing symmetric point $u=v=1$, where $u,v$ are conformally invariant cross ratios.…

High Energy Physics - Theory · Physics 2018-01-31 Wenliang Li