2023 Simons Collaboration on the Nonperturbative Bootstrap Annual Meeting

1       Overview

The seventh and last annual meeting of the Simons Collaboration on the Nonperturbative Bootstrap was our best attended ever. The meeting brought together 15 PIs, most of the collaboration postdocs, many graduate students, and a few guests from the New York area. As in past annual meetings, this final meeting was first and foremost an occasion for informal discussions.

The eight speakers this year were chosen to give a representative picture of the different research areas within the collaboration.

2       Abstracts of the Talks

• Tom Hartman: Averaged null energy and the renormalization group

  The averaged null energy operator is a light-ray integral of the null energy. This operator is known to be closely tied to causality in AdS/CFT, to deformations of the modular Hamiltonian in quantum field theory and to the Lorentzian inversion formula in CFT. I will discuss a new connection between averaged null energy and the monotonicity of the renormalization group in two and four dimensions. In particular, I will describe a new derivation of the c -theorem in two dimensions, and the a -theorem in four dimensions, from the averaged null energy condition, or ANEC. The derivation is based on contact terms that appear in correlation functions of the light-ray operator, and it hints at a more general role for Lorentzian inversion and light-ray operators in non-conformal QFTs.

• David Simmons-Duffin: Asymptotics of CFT Data

  Compactifying a CFT on a circle generically leads to a massive QFT in one lower dimension. Surprisingly, this simple observation makes several detailed predictions for the asymptotics of CFT data. I review the construction of the thermal effective action and the computation of the asymptotic density of states in higher dimensional CFTs. I then explain how to adapt this effective action to compute asymptotic OPE coefficients, and also “spin-refined” densities of states in general higher dimensional CFTs.

• Yifei He: Bootstrapping gauge theories (QCD)

  We consider asymptotically free gauge theories with gauge group SU ( N_c ) and N_f quarks with mass m_q « Λ QCD that undergo chiral symmetry breaking and confinement. We propose a bootstrap method to compute the S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy physics. For the important case of N_c = 3, N_f = 2, a numerical implementation of the method gives the phase shifts of the S0, P1 and S2 waves in good agreement with experimental results. The method incorporates gauge theory information ( N_c , N_f , m_q , Λ _QCD ) by using the form- factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules. At low energy, we impose constraints from chiral symmetry breaking. The only low-energy numerical inputs are the pion mass and the quark and gluon condensates. Based on 2309.12402 with Martin Kruczenski.

• Alessandro Vichi: Regge trajectories from pion scattering

  This seminar explores the EFT bootstrap formalism, leveraging dispersion relations to establish sum rules linking low-energy scattering amplitudes to high-energy partial wave expansion. We analyze the impact of different Regge behaviors at large energies and apply the formalism to study pion scattering at large N . Imposing the presence of spin-two states, we derive a mass bound for additional higher spin states, unveiling a kink structure. Investigation at this kink reveals intriguing agreements with real-world QCD observables.

• Miguel Paulos: Bootstrap systematics in one dimension

  The conformal bootstrap aims to solve CFTs using elementary assumptions. In this talk, I will describe the status of this program in its simplest possible setting.

• Simon Caron-Huot: Asymptotic measurements and crossing

  Why are scattering amplitudes analytic? After reviewing the conventional relation between momentums-pace analyticity and microcausality (vanishing of spacelike commutators), I will argue that analyticity of multi-point scattering amplitudes connects different types of asymptotic observables. These arise naturally from the commutators and differ from conventional amplitudes only by the operator ordering. Among applications, I will explain how this new perspective on crossing gives a new way to calculate in-in expectation values of physical interest, and discuss subtleties due to novel anomalous thresholds. Based on 2308.02125 and 2310.12199.

• Dalimil Ma z áč : New connections between harmonic analysis and conformal field theory

  I will discuss a connection between harmonic analysis on hyperbolic n -manifolds and conformal field theory in n − 1 dimensions. Used in one direction, this connection leads to new spectral bounds on hyperbolic manifolds. Used in the other direction, it offers a new viewpoint on the spectra data of conformal field theories.

• Liam Fitzpatrick: Lightcone Hamiltonian for Ising field theory

  Ising field theory in two dimensions provides probably the simplest example of a field theory without a Lagrangian description. We discuss why in general one should treat lightcone quantization as an effective theory of the infinite momentum frame with only a small subset of states remaining light, and we show how to integrate out all other states to generate the proper action for Ising field theory in lightcone quantization in the low temperature phase. We test our effective action extensively by comparing to a range of results from integrability and from TCSA. We also apply this method to the sine-Gordon model in 2D and discuss new effects that arise when the dimension of the interaction term is greater than d/ 2.