# Rigorous bounds on irrelevant operators in the 3d Ising model CFT

@inproceedings{Reehorst2021RigorousBO, title={Rigorous bounds on irrelevant operators in the 3d Ising model CFT}, author={Marten Reehorst}, year={2021} }

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 Z2-even scalar operators and ′ with a dimension below 6 we find a narrow allowed interval for ∆ ′ , λσσ ′ and λ ′ . With similar assumptions in the Z2-even spin-2 and the Z2-odd scalar sectors we are also able to constrain: the central charge cT ; the OPE data ∆T ′ , λ T ′ and λσσT ′ of the second spin-2 operator; and the OPE…

## Figures and Tables from this paper

## 5 Citations

The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap

- Mathematics
- 2021

: This paper studies the critical behavior of the 3d classical O( N ) model with a boundary. Recently, one of us established that upon treating N as a continuous variable, there exists a critical…

My title

- Mathematics
- 2022

A novel method for finding allowed regions in the space of CFT-data, coined navigator method, was recently proposed in [1]. Its efficacy was demonstrated in the simplest example possible, i.e. that…

Mixed correlator dispersive CFT sum rules

- MathematicsJournal of High Energy Physics
- 2022

Abstract
Conformal field theory (CFT) dispersion relations reconstruct correlators in terms of their double discontinuity. When applied to the crossing equation, such dispersive transforms lead to…

Snowmass White Paper: The Numerical Conformal Bootstrap

- Mathematics
- 2022

: We give a brief overview of the status of the numerical conformal bootstrap.

Bootstrapping Mixed MN Correlators in 3D

- Physics, Education
- 2021

The recent emergence of the modern conformal bootstrap method for the study of conformal ﬁeld theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by…

## References

SHOWING 1-10 OF 39 REFERENCES

The lightcone bootstrap and the spectrum of the 3d Ising CFT

- Mathematics
- 2016

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…

Precision islands in the Ising and O(N ) models

- Geology
- 2016

A bstractWe make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with…

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents

- Physics
- 2014

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge $$c$$c in…

The analytic bootstrap and AdS superhorizon locality

- Mathematics
- 2013

A bstractWe take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| ≪ |υ| < 1.…

Bootstrapping traceless symmetric $O(N)$ scalars

- Mathematics
- 2020

We use numerical bootstrap techniques to study correlation functions of a traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the…

New method for the conformal bootstrap with OPE truncations

- Mathematics
- 2017

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 $u,v$…

The Random-Bond Ising Model in 2.01 and 3 Dimensions

- Mathematics
- 2016

We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2<d<4 this disorder is a relevant…

Bootstrapping mixed correlators in the 3D Ising model

- Mathematics
- 2014

A bstractWe study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in…

Unitarity and the holographic S-Matrix

- Physics
- 2012

A bstractThe bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived…

Solving the 3D Ising Model with the Conformal Bootstrap

- Mathematics
- 2012

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…