## Abstract

We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the stress-tensor 4-point function and identify a non-redundant set of crossing equations. Studying these equations numerically using semidefinite optimization, we compute bounds on the central charge as a function of the independent coefficient in the stress-tensor 3-point function. With no additional assumptions, these bounds numerically reproduce the conformal collider bounds and give a general lower bound on the central charge. We also study the effect of gaps in the scalar, spin-2, and spin-4 spectra on the central charge bound. We find general upper bounds on these gaps as well as tighter restrictions on the stress-tensor 3-point function coefficients for theories with moderate gaps. When the gap for the leading scalar or spin-2 operator is sufficiently large to exclude large N theories, we also obtain upper bounds on the central charge, thus finding compact allowed regions. Finally, assuming the known low-lying spectrum and central charge of the critical 3d Ising model, we determine its stress-tensor 3-point function and derive a bound on its leading parity-odd scalar.

Original language | English |
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Article number | 164 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2018 |

### Bibliographical note

Publisher Copyright:© 2018, The Author(s).

## Keywords

- AdS-CFT Correspondence
- Conformal Field Theory
- Conformal and W Symmetry
- Field Theories in Higher Dimensions

## ASJC Scopus subject areas

- Nuclear and High Energy Physics