The conformal bootstrap: Theory, numerical techniques, and applications
Conformal field theories have been long known to describe the fascinating universal physics
of scale invariant critical points. They describe continuous phase transitions in fluids …
of scale invariant critical points. They describe continuous phase transitions in fluids …
The conformal bootstrap
D Poland, D Simmons-Duffin - Nature Physics, 2016 - nature.com
The conformal bootstrap was proposed in the 1970s as a strategy for calculating the
properties of second-order phase transitions. After spectacular success elucidating two …
properties of second-order phase transitions. After spectacular success elucidating two …
Precision islands in the Ising and O (N) models
A bstract We make precise determinations of the leading scaling dimensions and operator
product expansion (OPE) coefficients in the 3d Ising, O (2), and O (3) models from the …
product expansion (OPE) coefficients in the 3d Ising, O (2), and O (3) models from the …
Carving out OPE space and precise O (2) model critical exponents
A bstract We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting
surface” algorithm for scanning OPE coefficients makes it possible to find islands in high …
surface” algorithm for scanning OPE coefficients makes it possible to find islands in high …
The lightcone bootstrap and the spectrum of the 3d Ising CFT
D Simmons-Duffin - Journal of High Energy Physics, 2017 - Springer
We compute numerically the dimensions and OPE coefficients of several operators in the 3d
Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically …
Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically …
Weight shifting operators and conformal blocks
D Karateev, P Kravchuk, D Simmons-Duffin - Journal of High Energy …, 2018 - Springer
A bstract We introduce a large class of conformally-covariant differential operators and a
crossing equation that they obey. Together, these tools dramatically simplify calculations …
crossing equation that they obey. Together, these tools dramatically simplify calculations …
Scaling the semidefinite program solver SDPB
W Landry, D Simmons-Duffin - arXiv preprint arXiv:1909.09745, 2019 - arxiv.org
We present enhancements to SDPB, an open source, parallelized, arbitrary precision
semidefinite program solver designed for the conformal bootstrap. The main enhancement is …
semidefinite program solver designed for the conformal bootstrap. The main enhancement is …
[PDF][PDF] Snowmass White Paper: The Numerical Conformal Bootstrap
D Poland, D Simmons-Duffin - arXiv preprint arXiv:2203.08117, 2022 - arxiv.org
The idea of the conformal bootstrap is to constrain and solve CFTs using physical
consistency conditions like symmetry, unitarity, and causality. By relying on nonperturbative …
consistency conditions like symmetry, unitarity, and causality. By relying on nonperturbative …
The 3d stress-tensor bootstrap
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 …
preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of …
A proof of the conformal collider bounds
A bstract In this paper, we prove that the “conformal collider bounds” originally proposed in
[1] hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress …
[1] hold for any unitary parity-preserving conformal field theory (CFT) with a unique stress …