The 3d stress-tensor bootstrap

• Published in: The journal of high energy physics 2018-02, Vol.2018 (2), p.1-48, Article 164
• Main Authors: Dymarsky, Anatoly, Kos, Filip, Kravchuk, Petr, Poland, David, Simmons-Duffin, David
• Format: Article
• Language: English
• Subjects: AdS-CFT Correspondence; Classical and Quantum Gravitation; Conformal and W Symmetry; Conformal Field Theory; Elementary Particles; Field Theories in Higher Dimensions; High energy physics; Ising model; Lower bounds; Mathematical models; Operators (mathematics); Parity; Permutations; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Stress tensors; String Theory; Symmetry; Tensors; Upper bounds
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2018)164

A bstract 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.