2022 Simons Collaboration on the Nonperturbative Bootstrap Annual Meeting

1. Overview
 

The sixth annual meeting of the Simons Collaboration on the Non-perturbative Bootstrap was one of the best attended so far, with 104 in-person participants. The meeting brought together 14 PIs, most of the Collaboration postdocs, many graduate students, and a few guests from the New York area. As in past editions, 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
 

• Slava Rychkov: Twist accumulation in conformal field theory: a rigorous approach to the lightcone bootstrap

We will present a rigorous proof that any unitary CFT in two or higher dimensions, with a positive twist gap in the spectrum of global conformal group primaries, contains infinite families of primary operators whose spin grows to infinity while the twist approaches a constant limit. Joint work with Sridip Pal and Jiaixin Qiao.
 

• Ning Su: Skydiving to Bootstrap Islands: an Algorithm for Dynamically Constrained SDP

The numerics of the semidefinite program (SDP) is the most time consuming part of a large scale conformal bootstrap computation. In this talk, I will present a new algorithm to overcome this bottleneck. In the old method, one has to solve many SDPs, each corresponding to a point in the theory space. The new algorithm treats the optimization in the theory space and the optimization of the SDP as a single problem and solves both simultaneously. The average number of iterations spent on each point is much less than the old method. Therefore many bootstrap setups that were practically impossible to compute will be do-able in the near future. I will discuss some of those setups and show how the new algorithm can help us answer interesting physics questions.
 

• Zohar Komargodski: Large Quantum Numbers: from Large Charge to Large Spin through a Large Vortex

We make a proposal for a new phase, the “giant vortex,” describing an intermediate regime with large spin and charge. The new phase connects superfluid theory with the large-spin expansion. The giant vortex admits a semi-classical effective theory description with peculiar chiral excitations (moving at the speed of light) and a Fock space of states that is reminiscent of the multi-twist operators in Regge theory, including the leading and daughter Regge trajectories. We show that the transition from the giant vortex to the Regge regime is accompanied by the scaling dimension turning from being larger than to being smaller than the mean field theory value, i.e. gravity switches from being the weakest force at small AdS distance to being the strongest force at large AdS distance.
 

• Xi Yin : Solving lattice quantum field theories with convex optimization

I discuss how lattice quantum field theory may be solved by convex optimization, based on Schwinger- Dyson equations and reflection positivity, exemplified through the Ising model on 2D square lattice and 3D cubic lattice. I also discuss an analogous approach to classical dynamical systems.
 

• Ami Katz: Thermalization and chaos in a 1+1d QFT

We study aspects of chaos and thermodynamics at strong coupling in a 1+1d QFT using numerical Hamiltonian truncation methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix statistics both at weak and strong coupling. We also find scar states, but only at weak coupling. We then use these chaotic states to compute thermodynamic observables, obtaining results consistent with CFT expectations at temperatures above the scale of relevant interactions. Finally, we test the Eigenstate Thermalization Hypothesis in a new regime by being able to access the expectation value of local QFT operators in eigenstates with high energy densities. These expectation values show universality and are found to be consistent with analytic finite temperature CFT results.
 

• SIlviu Pufu: Discrete chiral symmetry and mass shift in lattice Hamiltonian approach to Schwinger model

The Schwinger model, or quantum electrodynamics in 1+1 dimensions, is one of the simplest gauge theories. In this talk, I will first review a standard lattice discretization of this theory using the Kogut-Susskind Hamiltonian approach with staggered fermions. I will then present a new relation between the lattice and continuum mass parameters, and show how this relation significantly improves the continuum extrapolations of various quantities computed on the lattice.
 

• Simon Caron-Huot: Holographic cameras: an eye for the bulk

We consider four-point correlators in an excited quantum state of a field theory. We show that when the theory and state are holographic, these correlators can produce high-quality images of point- like bulk particles, revealing the geometry in which they move. In theories or states that are not holographic, the images are too blurry to extract a bulk geometry. Calculations are performed by adapting formulas from conformal Regge theory to excited states.
 

• Pedro Vieira: The Light Side of the Complex Spin Plane and Newton’s Dark Magic

Conformal Regge theory predicts the existence of analytically continued CFT data for complex spin. How could this work when there are so many more operators with large spin compared to small spin? Using planar N=4 SYM as a testground we find a simple physical picture. Operators do organize themselves into analytic families but the continuation of the higher families have zeroes in their structure OPE constants for lower integer spins. They thus decouple. Newton’s interpolation series technique is perfectly suited to this physical problem and will allow us to explore the right complex spin half-plane.