Simons Collaboration on the Nonperturbative Bootstrap Annual Meeting 2020

Leonardo Rastelli
YITP, Stony Brook
Director’s Overview

I will start with an overview of the structure of the Collaboration and of our research activities and main areas of progress in the past year. I will then focus on some more specific developments in the analytic and holographic bootstrap.

David Poland
Yale University
Progress in the Conformal Bootstrap
View Slides (PDF)

I will describe progress that our collaboration has made in the conformal bootstrap. New software tools and algorithms have enabled the study of much larger systems of bootstrap equations, allowing us to expand and refine the map of conformal field theories. In particular, these methods have led to precise numerical solutions of
the 3d O(N) models, resolving longstanding questions in these theories. Complementary progress has been made in the application of analytical methods such as the Lorentzian Inversion formula, where one sees excellent agreement between numerical and analytical solutions.

Joao Penedones
EPFL
Progress in the S-matrix Bootstrap
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I will briefly motivate the bootstrap approach for non-conformal theories and review the (primal) numerical S-matrix bootstrap. Then, I will describe the main developments of the last year:

i) The formulation of a dual S-matrix bootstrap (in 2D QFT) that leads to rigorous bounds with finite numerical truncation.
ii) The generalization of the S-matrix bootstrap to include states created by acting with local operators on the vacuum. This involves form factors and spectral densities. In particular, in 2D QFT, it gives access to the central charge of the UV CFT.
iii) The application of the numerical S-matrix bootstrap to bound Wilson coefficients in Effective Field Theories. I will discuss the recent application to the chiral lagrangian describing the low energy dynamics of massless pions.

Consequences of Conformality

Balt van Rees, Ph.D.
Professor, École Polytechnique

Wednesday November 11, 2020
Online
4:45 – 5:00 PM ET Webinar waiting room opens
5:00 – 6:15 PM ET Talk + Q&A

In the phase diagrams of many substances (such as water, helium and magnets), there are ‘critical’ points with remarkable physical properties. Mathematically these points exhibit a high degree of symmetry known as ‘conformal invariance.’ In this lecture, Balt van Rees will discuss how conformal invariance can emerge, why they can be used to make precise and quantitative predictions, and what remains to be done to understand their consequences fully.

The research update PDF may be downloaded here.