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Title: The 3d stress-tensor bootstrap

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]; ORCiD logo [3];  [4];  [5]
  1. Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy; Skolkovo Inst. of Science and Technology, Moscow (Russian Federation). Skolkovo Innovation Center
  2. Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics and Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
  3. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  4. Yale Univ., New Haven, CT (United States). Dept. of Physics
  5. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
+ Show Author Affiliations

Here, 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.

Research Organization:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Scientific User Facilities Division; National Science Foundation (NSF); Simons Foundation
Grant/Contract Number:
SC0009988; SC0011632; AC02-05CH11231
OSTI ID:
1461289
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2018; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (26)

Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey journal March 2018
From spinning conformal blocks to matrix Calogero-Sutherland models journal April 2018
autoboot: a generator of bootstrap equations with global symmetry journal June 2019
Fermion conformal bootstrap in 4d journal June 2019
Beyond a = c : gravitational couplings to matter and the stress tensor OPE journal July 2018
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory journal July 2018
Higher spin ANEC and the space of CFTs journal July 2019
Graviton scattering and a sum rule for the c anomaly in 4D CFT journal September 2018
Scalar CFTs and their large N limits journal September 2018
Harmonic analysis and mean field theory journal October 2019
Bootstrapping the minimal 3D SCFT journal November 2018
R-current three-point functions in 4d N$$ \mathcal{N} $$ = 1 superconformal theories journal December 2018
Recursion relation for general 3d blocks journal December 2019
Bootstrapping the long-range Ising model in three dimensions journal January 2019
Bounds on amplitudes in effective theories with massive spinning particles journal August 2018
The conformal bootstrap: Theory, numerical techniques, and applications journal January 2019
From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models text January 2017
From spinning conformal blocks to matrix Calogero-Sutherland models text January 2018
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory text January 2018
Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey text January 2017
Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory text January 2017
Scalar CFTs and Their Large N Limits text January 2017
Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE text January 2017
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text January 2018
Bootstrapping the long-range Ising model in three dimensions text January 2018
autoboot: A generator of bootstrap equations with global symmetry preprint January 2019

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