Simons Collaboration on the Nonperturbative Bootstrap Annual Meeting 2021

Bootstrap Collaboration Annual Meeting 2021
 

1 Overview

The fifth annual meeting of the Simons Collaboration on the Non-Perturbative Bootstrap was the first in-person meeting of the Collaboration since the start of the COVID-19 pandemic. Despite the still difficult global-travel situation, it was remarkably well attended, with 90 in-person participants, a dozen of whom arrived from Europe; in addition, 55 participants registered to attend remotely. The meeting brought together 13 PIs (with the other 4 attending remotely), most of the Collaboration postdocs, many graduate students, and a few guests from the New York area. As in past editions, but more so given the long hiatus of in-person activities, the meeting was first and foremost an occasion for informal discussions.
The eight speakers were chosen to give a representative picture of the different research areas within the Collaboration.
 

2 Abstracts of the Talks

• David Poland: Advancing the Conformal Frontier

David Poland reviewed progress from the past year mapping out and solving conformal field theories using the conformal bootstrap. Including new bounds on the 3d O(3) model, which has given a bootstrap proof that critical Heisenberg magnets are unstable to cubic anisotropy, new precision islands in the supersymmetric Ising and 3d Gross-Neveu-Yukawa models, and new constraints on 4-flavor 3d quantum electrodynamics.
 

• Balt van Rees: QFT in AdS, the Flat-Space Limit, and the Bootstrap

Putting quantum field theories on a hyperbolic spacetime leads to many interesting questions. Balt van Rees discussed how, under mild assumptions, the boundary correlation functions remain conformally invariant even along an RG flow. In the flat-space limit, these conformal observables become the S-matrix elements, and van Rees explained how to take this limit and what kind of subtleties arise. Lastly, van Rees presented an attempt at using the numerical conformal bootstrap to analyze an RG flow between minimal models.
 

• Pedro Vieira: Conformal Stampedes

Some quantities in gauge theory are dominated by so-called leading logs and can be re-summed to all loop orders. Pedro Vieira introduced the notion of a stampede, which is a simple time evolution of a bunch of particles that start their life in a corner – on the very right say – and hop their way to the opposite corner – on the left – through the repeated action of a quantum Hamiltonian. Such stampedes govern some leading logs quantities in quantum field theories. The leading Euclidean OPE limit of correlation functions in the fishnet theory and null limits of correlators in N = 4 SYM in interesting double-scaling limits are notable examples. As an application, based on upcoming work with Enrico Olivucci, Vieira used these results to extend the beautiful bootstrap program of Coronado to all octagon correlators with arbitrary diagonal bridge length.
 

• Zohar Komargodski: Defect Conformal Field Theories and Renormalization Group Flows

Zohar Komargodski reviewed the subject of line defects in d-dimensional conformal field theories (CFTs). Komargodski discussed an exact formula governing the renormalization group flow online defects and considered some examples involving line defects in 2, 3, and 4 space-time dimensions.
 

• Liam Fitzpatrick: Extracting QFT Dynamics from CFT Data with Lightcone Conformal Truncation

In this talk, Liam Fitzpatrick described recent progress in applying Hamiltonian truncation methods in lightcone quantization using a conformal basis. In addition, Fitzpatrick described how combining this method with the S-matrix bootstrap, and a recent generalization of it that involves spectral densities and form factors, one can efficiently extract precise scattering amplitudes in 2d φ 4 theory for couplings that range from the perturbative regime up to near the critical point.
 

• Simon Caron-Huot: Causality Constraints on Gravity

Effective field theories (EFT) are widely used to parameterize long-distance effects of unknown short distance dynamics or possible new heavy particles. It is known that EFT parameters are not entirely arbitrary and must obey positivity constraints if causality and unitarity are satisfied at all scales. Simon Caron-Huot systematically explored those constraints from the perspective of 2-to-2 scattering processes and show that all EFT parameters in units of the mass threshold M are bounded below and above: causality requires a sharp form of dimensional analysis scaling. The bounds are particularly restrictive for gravity due to its rapid energy growth at tree-level; Caron-Huot presented model-independent limits on modifications of four-dimensional Einstein’s gravity in terms of the mass M of higher-spin particles.
 

• Thomas Hartman: Averaged CFTs and Holography

Recent developments suggest that the sum over topologies in quantum gravity is related to an average over coupling constants, at least in certain models. Thomas Hartman described an interacting toy model in 2d CFT where this can be studied in detail. The boundary theory is a WZW model averaged over exactly marginal deformations, and the bulk theory is a Chern-Simons-like theory in three dimensions. Hartman also argued that wormhole topologies in quantum gravity suggest a new direction for the analytic bootstrap.
 

• Dalimil Mazáč: Geometric Bootstrap

Dalimil Mazáč explained how the conformal bootstrap can be adapted to place bounds on the spectrum of the Laplacian on hyperbolic surfaces and orbifolds. Each hyperbolic surface gives rise to a Hilbert space which is a unitary representation of G=PSL(2,R). Furthermore, this Hilbert space carries a natural G-invariant product, analogous to the OPE. One can then define the notions of local operators, correlation functions and conformal blocks, and derive appropriate bootstrap equations. Mazáč used this method to prove upper bounds on the lowest positive eigenvalue of the Laplacian on all closed hyperbolic surfaces of a fixed genus. The bounds at genus 2 and genus 3 are very nearly saturated by the Bolza surface and the Klein quartic.

Thomas Hartman
Cornell University

Black Holes and Quantum Gravity

Black holes have mysterious properties that indicate that they are composed of an enormous number of microscopic parts. This has led to the idea that in quantum gravity, spacetime itself emerges from something more fundamental.

In this lecture, Thomas Hartman will describe how black holes provide a window into quantum gravity and how scientists use the ‘bootstrap’ technique to study them. This line of research leads from black hole thermodynamics to the notorious sphere packing problem in mathematics, first studied by Johannes Kepler and contemporaries four centuries ago.