Simons Collaboration on the Nonperturbative Bootstrap Annual Meeting 2018

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The second annual meeting of the Simons Collaboration on the Non-perturbative Bootstrap brought together all the 17 PIs, most of the postdocs and many graduate students of the Collaboration. The meeting was very well attended, with over 80 participants internal to the Collaboration and several guests from the New York area.

The speakers were chosen to give a representative picture of the different research areas within the Collaboration, ranging from the conformal bootstrap program, both in its numerical and analytic aspects (Rychkov, Poland, Simmons-Duffin), the holographic bootstrap (Caron-Huot, Fitzpatrick, Pufu), the S-matrix bootstrap (Penedones), the exact supersymmetric bootstrap (Rastelli, Komargodski, Pufu), and conformal truncation methods (Katz).

The meeting also provided the opportunity to introduce our recently hired software engineer (Walter Landry) to the whole Collaboration. He gave a progress report on his impressive improvements of the numerical codes for the conformal bootstrap.

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After mentioning some of the numerical bootstrap highlights of this year (see also David Poland’s talk), Rychkov presented some targets for future work. Some of these targets came to our attention during the work on the numerical conformal bootstrap review (Poland, Rychkov, Vichi 1805.04405, to appear in Reviews of Modern Physics). Others reflect interesting RG stability phenomena in multiscalar field theories with reduced symmetry groups, predicted 40 years ago in the work of L. Michel and collaborators. At the end of the presentation, Walter Landry reported on dramatic performance improvements made in numerical codes to generate conformal blocks and solve the semidefinite problem.

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Poland reviewed progress at using the numerical conformal bootstrap to find the sequence of 3D CFTs known as the Gross-Neveu-Yukawa models, describing fixed points involving N interacting fermions. When N = 1, there exists a supersymmetric fixed point which has been proposed to be potentially realizable on the boundaries of topological superconductors. He described recent progress at isolating this minimal 3D SCFT using the numerical bootstrap, yielding high precision determinations of its leading scaling dimensions and OPE coefficients. These determinations show a remarkable consistency with being expressible in terms of the transcendental number tan(1).

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Through the AdS/CFT correspondence, the conformal bootstrap offers a powerful tool to study gravitational theories. Caron-Huot reviewed the computation of correlators of all single-trace primaries in maximally supersymmetric Yang-Mills theory, focusing on the limit of large N and strong coupling where it is dual to supergravity in AdS₅ × S⁵ geometry. The correlators turn out to unify into a single object, thanks to a surprising symmetry of the gravitational dynamics. Based on 1809.09173.

In Euclidean signature, the operator product expansion (OPE) provides a powerful tool for non-perturbative computations of correlation functions, and is at the heart of the conformal bootstrap program. However, in Lorentzian signature, there are many interesting observables where the traditional OPE doesn’t apply or converges badly. In this talk, Simmons-Duffin described light-ray operators – a new class of objects that allow for new types of Lorentzian OPEs. He focused on the Regge limit of correlators, and also briefly discussed collider event shapes.

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Rastelli gave on overview of the chiral algebra program for 4d N = 2 superconformal field theories (SCFTs). To any N = 2 SCFT, one can canonically associate a 2d chiral algebra. Rastelli illustrated the basics of this 4d/2d correspondence in a few simple examples. The talk emphasized the use of this correspondence as an organizing principle for the whole landscape of 4d N = 2 theories. We are learning that chiral algebras that arise from 4d SCFTs are very special. They capture the effective field theory at a generic point of the Higgs branch and are strongly constrained by the requirement of 4d unitarity. The effective field picture leads to remarkable free-field realizations of (seemingly) all chiral algebras that descend from N = 2 SCFTs. A classification program appears within reach.

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After reviewing some challenges associated with equal time quantization, Katz discussed how these can be avoided by light-cone quantization. On the light-cone, however, one faces the problem of incorporating the effects of so called ?light-cone zero modes.? Katz described the proposal of a prescription for accounting for the zero-modes and check this prescription in various 2D and 3D cases.

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Penedones reviewed the recent work on the S-matrix bootstrap of four dimensional scattering amplitudes with O(3) symmetry and no bound-states. Penedones and collaborators explored the allowed space of scattering lengths which parametrize the interaction strength at threshold of the various scattering channels, and considered an application of this formalism to pion physics. A signature of pions is that they are derivatively coupled leading to (chiral) zeros in their scattering amplitudes. Penedones et al. explored the multi-dimensional space of chiral zeros positions, scattering length values and resonance mass values. Interestingly, they encountered lakes, peninsulas and kinks depending on which sections of this intricate multi-dimensional space we consider. QCD seems to lie at a remarkable location in these plots, based on various experimental and theoretical expectations.

Komargodski reviewed the program of the Coulomb branch bootstrap, and its various applications to related subjects, such as resurgence, integrability, and AdS/CFT. He outlined some interesting recent progress concerning numerical results from the Bootstrap and from the large charge expansion technique. He also discussed important open problems, mostly concerning with non-Lagrangian theories.

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Fitzpatrick discussed how to obtain dynamics of semiclassical gravity in 3d AdS from the large central charge limit of irreducible representations of the conformal algebra of 2d CFTs, with a focus on black hole information loss and bulk reconstruction. He described recent and ongoing work to extract ‘non-perturbative’ (in Newton’s constant) gravitational effects from the exact behavior of such irreps at large but finite central charge.

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Pufu described recent progress in relating exact results in CFTs to scattering amplitudes of gravitons and their superpartners in M-theory and type II string theory. In particular, he showed how one can recover the first few terms in the small momentum expansion of these scattering amplitudes from CFT and present new results for the CFT data of both 3d and 4d maximally supersymmetric CFTs at strong coupling.