The 3d stress-tensor bootstrap

Anatoly Dymarsky, Filip Kos, Petr Kravchuk, David Poland, David Simmons-Duffin

Research output: Contribution to journalArticlepeer-review

63 Scopus citations

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 languageEnglish
Article number164
JournalJournal of High Energy Physics
Volume2018
Issue number2
DOIs
StatePublished - 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

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