# More analytic bootstrap: nonperturbative effects and fermions

@article{Albayrak2019MoreAB, title={More analytic bootstrap: nonperturbative effects and fermions}, author={Soner Albayrak and David Meltzer and David Poland}, journal={Journal of High Energy Physics}, year={2019} }

Abstract
We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show that these effects are important for precision applications of the analytic bootstrap in the context of the 3d Ising and O(2) models. In the former they allow us to reproduce the spin-2 stress tensor with error at the 10−5 level while in the…

## 38 Citations

### Analytic bootstrap of mixed correlators in the O(n) CFT

- MathematicsJournal of High Energy Physics
- 2022

We use large spin perturbation theory and the Lorentzian inversion formula to compute order-ϵ corrections to mixed correlators in the O(n) Wilson-Fisher CFT in 4 − ϵ dimensions. In particular, we…

### The inversion formula and 6j symbol for 3d fermions

- PhysicsJournal of High Energy Physics
- 2020

Abstract
In this work we study the 6j symbol of the 3d conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with…

### Analytic bootstrap of mixed correlators in the $\boldsymbol{O(n)}$ CFT

- Mathematics
- 2022

: We use large spin perturbation theory and the Lorentzian inversion formula to compute order- ε corrections to mixed correlators in the O ( n ) Wilson–Fisher CFT in 4 − ε dimensions. In particular,…

### Regge trajectories for the (2, 0) theories

- Mathematics, PhysicsJournal of High Energy Physics
- 2022

We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2 , 0) theories in six dimensions. The different conformal multiplets in a single superconformal…

### The leading trajectory in the 2+1D Ising CFT

- Mathematics
- 2020

We study the scattering of lumps in the 2+1-dimensional Ising CFT, indirectly, by analytically continuing its spectrum using the Lorentzian inversion formula. We find evidence that the intercept of…

### Closed-form expression for cross-channel conformal blocks near the lightcone

- MathematicsJournal of High Energy Physics
- 2020

In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point functions…

### Holographic thermal correlators from supersymmetric instantons

- Physics
- 2022

We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation…

### Bootstrapping $N_f=4$ conformal QED$_3$

- Physics
- 2021

We present the results of a conformal bootstrap study of the presumed unitary IR xed point of quantum electrodynamics in three dimensions (QED3) coupled to Nf = 4 two-component Dirac fermions. Speci…

### AdS/CFT unitarity at higher loops: high-energy string scattering

- PhysicsJournal of High Energy Physics
- 2020

What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet…

### The Hybrid Bootstrap

- Computer Science
- 2022

This work discusses the general strategy to perform such a hybrid bootstrap, and makes a partial implementation of the strategy for 3D Ising CFT {σ, } system.

## References

SHOWING 1-10 OF 50 REFERENCES

### Conformal bootstrap in the Regge limit

- Mathematics
- 2017

A bstractWe analytically solve the conformal bootstrap equations in the Regge limit for large N conformal field theories. For theories with a parametrically large gap, the amplitude is dominated by…

### Bootstrapping 3D fermions

- Physics
- 2015

A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in…

### Bootstrapping 3D fermions with global symmetries

- Mathematics
- 2017

A bstractWe study the conformal bootstrap for 4-point functions of fermions 〈ψiψjψkψℓ〉 in parity-preserving 3d CFTs, where ψi transforms as a vector under an O(N ) global symmetry. We compute bounds…

### Fermion conformal bootstrap in 4d

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE…

### Scalar-fermion analytic bootstrap in 4D

- PhysicsJournal of High Energy Physics
- 2019

A bstractIn this work we discuss an analytic bootstrap approach [1, 2] in the context of spinning 4D conformal blocks [3, 4]. As an example we study the simplest spinning case, the scalar-fermion…

### Analyticity in spin in conformal theories

- Mathematics
- 2017

A bstractConformal theory correlators are characterized by the spectrum and three-point functions of local operators. We present a formula which extracts this data as an analytic function of spin. In…

### Comments on operators with large spin

- Physics
- 2007

We consider high spin operators. We give a general argument for the logarithmic scaling of their anomalous dimensions which is based on the symmetries of the problem. By an analytic continuation we…

### Mellin space bootstrap for global symmetry

- Mathematics
- 2016

A bstractWe apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with O(N) symmetry and cubic anisotropy. We write down the conditions arising from the consistency…

### An algebraic approach to the analytic bootstrap

- Mathematics
- 2015

A bstractWe develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired…

### Bootstrapping the minimal N = 1 superconformal field theory in three dimensions

- Physics
- 2018

We develop the numerical bootstrap technique to study the 2 + 1 dimensional N = 1 superconformal field theories (SCFTs). When applied to the minimal N = 1 SCFT, it allows us to determine its critical…