# 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…

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## 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…

### Conformal collider physics from the lightcone bootstrap

- Physics
- 2015

A bstractWe analytically study the lightcone limit of the conformal bootstrap equations for 4-point functions containing global symmetry currents and the stress tensor in 3d CFTs. We show that the…

### 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…

### 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…