Positivity and the Bootstrap

31 May 2021, 14:30 → 2 Jun 2021, 18:00 Europe/Zurich

ONLINE only (CERN)

This will be a short informal workshop to bring together researchers interested in amplitude positivity and its applications.  It will be spread over three days and cover recent developments in formal, cosmological, and phenomenological areas.  There will be one day each on cosmo, pheno, formal, with three talks each day and some informal discussion in between.

 

Organisers: Brando Bellazzini (IPHT and CERN), Matthew McCullough (TH), Andrea Puhm (CPHT), Sasha Zhiboedov (TH).

 

Monday, 31 May

1 Positivity without Boosts: UV/IR Relations for Cosmology

Positivity bounds are a powerful tool which can connect IR phenomenology with the underlying fundamental physics in the UV, but to date their implementation has required Lorentz invariance at all scales.
This talk describes recent progress in removing this assumption, deriving a set of bounds which can be applied to systems in which boosts are spontaneously broken, such as cosmology.
For example, these new bounds place UV constraints on the shapes of cosmological correlators in the CMB which can arise from the effective field theory of single-field inflation.

Speaker: Scott Melville

Melville_Positivity_31May2021_NoTransitions.pdf

Recording

2 A Timeless History of Time

Cosmological observations give us the unique opportunity to probe the fundamental laws of physics at very high energies as well as the perturbative regime of quantum gravity. Unfortunately, due to the creativity of theorists and the paucity of data about the primordial universe, there is a huge number of models compatible with all measurements, featuring a wide variety of mechanisms, symmetries, and spectra of particles.The reason can be traced back to the fact that we don't observe the time evolution during inflation, but only its final outcome.
In this talk I will report on the recent progress in developing a completely new "bootstrap" approach to derive predictions from the very early universe that make no reference to time and the un-observable time evolution. The bootstrap approach builds directly upon the fundamental pillars of physics. In particular, I will present the recent breakthroughs in understanding the consequence of unitarity for cosmological correlators to all orders in perturbation theory, as well as the footprint of (bulk) locality. I will show how these principles can be used to derive many classical and new inflationary predictions associated with primordial non-Gaussianity in a way that is both computationally simpler and conceptually more transparent. This includes a reconstruction formula that relates de Sitter correlators to amplitudes for massless particles, cosmological partial-energy recursion relations and a "timeless" differential representation of the perturbative wavefunction. This approach makes no reference to de Sitter boosts, which are broken by a large amount in models that predict large non-Gaussianity. Finally I speculate on how these results give us a handle on non-perturbative effects in cosmology either from cosmological positivity bounds or from de Sitter holography.

Speaker: Enrico Pajer (University of Cambridge)

Recording

3 On analytic properties of cosmological correlators

Speaker: Viktor Gorbenko

Positivity, bootstrap.pdf

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4 Discussion

Speaker: Claudia de Rham (Imperial College London)

Recording

Tuesday, 1 June

5 Positivity bounds in SMEFT and the inverse problem.

Speaker: Cen Zhang (Institute of High Energy Physics, Chinese Academy Sciences)

2021June.pdf

Recording

6 The facets of product moments: from EFThedron to Modularhedron

Speaker: yu-tin Huang

Recording

Yutinpdf.pdf

7 Positive Moments and Loops

Speaker: Francesco Riva

CERNbootstrap.pdf

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8 Discussion

Speaker: Joao Miguel Augusto Penedones Fernandes (EPFL - Ecole Polytechnique Federale Lausanne (CH))

Recording

Wednesday, 2 June

9 Rigorous bounds on the analytic S-matrix

In this talk I will introduce a complementary approach to the non-perturbative S-matrix Bootstrap based on duality in optimization theory.
In particular, I will focus on the problem of bounding the quartic coupling for gapped theories in 4-dimensions, both from above and below.
The bounds obtained rely solely on proven analyticity properties and the numerical problem can be efficiently solved using SDPB.

Speaker: Andrea Guerrieri

Recording

10 Celestial amplitudes: from UV constraints to conformal blocks

Celestial amplitudes describe scattering in a basis of boost eigenstates. In this basis, 4-point scattering is characterized by two variables: the sum over the boost weights $\beta$ which is dual to the center of mass energy, and a cross ratio $z$ related to the bulk scattering angle. In this talk I will describe two aspects of the physics captured by the $\beta$ and $z$ dependence. I will first show that the UV behavior of 4-point scattering is encoded in the analytic structure of celestial amplitudes in the complex $\beta$ plane. The residues of the poles at negative even integer $\beta$ are related to coefficients of higher-dimension operators in the low-energy effective action hence subject to positivity constraints, while poles at positive even integer $\beta$ arise from UV asymptotics. I will then show that the $z$ dependence contains information about the celestial spectrum and three-point couplings. For scalar 4-point scattering mediated by massive exchange, the conformal blocks include massive scalar states with positive integer conformal weights, as well as intermediate exchanges of spinning light-ray states.

Speaker: Raclariu Ana-Maria

CERN-final.pdf

Recording

11 Positive sum rules in gravitational EFTs

We explore constraints on low-energy dynamics which stem from assuming causality of 2->2 scattering at all energy scales. I will review a key ingredient added recently: low-energy crossing symmetry, which bounds the couplings of spinning heavy states and ensures that sum rules are dominated by (unknown) states of low spin. Gravity is special since its tree-level energy growth already requires a UV completion. This implies roughly that gravity is attractive at all scales. I describe model-independent constraints which exploit low-energy crossing to account for the graviton pole.

Speaker: Simon Caron-Huot

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12 Discussion

Speaker: Andrew Tolley (Imperial College London)

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