Positivity and the Bootstrap





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).


  • Admir Greljo
  • Ahmadullah Zahed
  • Akhil Premkumar
  • Alejandra Castro
  • Alejo Rossia
  • Aleksandr Zheltukhin
  • Alessandra Gnecchi
  • Alessandro Georgoudis
  • Alessandro Vichi
  • Alexander Söderberg
  • Alexander Zhiboedov
  • Allic Sivaramakrishnan
  • Amirhossein Tajdini
  • Amit Sever
  • Amjad Ashoorioon
  • Anastasia Volovich
  • Andrea Guerrieri
  • Andrea Puhm
  • Andrei Parnachev
  • Andrew Tolley
  • Angelo Esposito
  • Anh-Khoi Trinh
  • Aninda Sinha
  • Anna Tokareva
  • Bartolomeo Fiorini
  • Benjamin Grinstein
  • Biswajit Sahoo
  • Brando Bellazzini
  • Brian Henning
  • Brian McPeak
  • Bruce Campbell
  • Carlos Duaso Pueyo
  • Carlos Rodriguez
  • Cen Zhang
  • Cezar Condeescu
  • Chen Yang
  • Chia-Hsien Shen
  • Christophe Grojean
  • Claudia de Rham
  • comelli denis
  • Costas Bachas
  • Da Liu
  • Dalimil Mazac
  • Daniel Mayerson
  • David Meltzer
  • David Stefanyszyn
  • Davide Maria Lombardo
  • Dean Carmi
  • Denis Karateev
  • Diederik Roest
  • Diego Blas Temino
  • Diego Redigolo
  • Dimitrios Kosmopoulos
  • Dong-Gang Wang
  • Elias Kiritsis
  • Elliot Leader
  • Emanuele Gendy Abd El Sayed
  • Emilian Dudas
  • Emilio Trevisani
  • Enrico Herrmann
  • Faizan Bhat
  • Federico Gasparotto
  • Filippo Vernizzi
  • Francesco D'Eramo
  • Francesco Russo
  • Francesco Serra
  • Francesco Sgarlata
  • Gabor Sarosi
  • Gabriel Lefundes
  • Gabriele Di Ubaldo
  • Gauthier Durieux
  • German Rodrigo
  • Gianbattista-Piero Nicosia
  • Giovanni Tambalo
  • Giovanni Venturi
  • Giulia Fardelli
  • Giulia Isabella
  • Grant Remmen
  • Gregory Loges
  • Hidetoshi Omiya
  • Hoiki Liu
  • Hongbin Chen
  • Hongliang Jiang
  • Hugh Osborn
  • Humberto Gomez
  • Hyun Min Lee
  • Igor Mol
  • Iosif Bena
  • Jamal Jalilian-Marian
  • James Bonifacio
  • Jan de Boer
  • Javi Serra
  • Jeevan Chandra Namburi
  • Jiaxin Qiao
  • Jiayin Gu
  • Joan Elias Miro
  • Joao Penedones
  • Johan Henriksson
  • Julio Parra-Martinez
  • Junsei Tokuda
  • Jure Zupan
  • Katsuki Aoki
  • Keigo Shimada
  • Kelian Philippe Haring
  • Kentarou Mawatari
  • Kimiko Yamashita
  • Konstantinos Rigatos
  • Kostas Skenderis
  • Kuo-Wei Huang
  • Kurt Hinterbichler
  • Lars Aalsma
  • Laura Johnson
  • Leandro Da Rold
  • Leonardo Trombetta
  • Lorenzo Di Pietro
  • Lucia Cordova
  • Manoj Kumar Mandal
  • Manuel Loparco
  • Marc Riembau
  • Marco Meineri
  • Marco Radici
  • Marco Serone
  • Marcus Spradlin
  • Mariia Savina
  • Marija Tomasevic
  • Mario Herrero Valea
  • Marko Simonovic
  • Masahito Yamazaki
  • Massimo Pietroni
  • Matteo Sergola
  • Matthew Lewandowski
  • Matthew Philip Mccullough
  • Matthew Thomas Walters
  • Matthias Volk
  • Michele Santagata
  • Miguel Alexandre Ribeiro Correia
  • Mikhail Isachenkov
  • Mindaugas Karciauskas
  • Mohammad Ali Gorji
  • Mudassir Moosa
  • Nicholas Rodd
  • Nidhi Sudhir
  • Oliver Janssen
  • Paolo Creminelli
  • Paolo Pichini
  • Pere Talavera
  • Piotr Bargiela
  • Piotr Tourkine
  • Piyabut Burikham
  • Plamen Fiziev
  • Pranjal Nayak
  • Quang Loc Tran
  • Quentin Bonnefoy
  • Rachel Rosen
  • Raghu Mahajan
  • Rajeev Singh
  • Ritabrata Bhattacharya
  • Ross Glew
  • Sadra Jazayeri
  • Satoshi Mishima
  • Savan Kharel
  • Scott Collier
  • Scott Melville
  • Sebastian Cespedes
  • Shota Komatsu
  • Shuang-Yong Zhou
  • Shuntaro Aoki
  • Silvia Nagy
  • Simon Caron-Huot
  • Sohyun Park
  • Soubhik Kumar
  • Spencer Chang
  • Subramanya Hegde
  • Suro Kim
  • Sébastien Renaux-Petel
  • Takahiro Terada
  • Takeshi Kobayashi
  • Tanguy Grall
  • Tania Robens
  • Tevong You
  • Till Heckelbacher
  • Tim Morris
  • Tom Hartman
  • Tom Melia
  • Tomo Takahashi
  • Toshifumi Noumi
  • Tzu-Chen Huang
  • Urs Wiedemann
  • Vicharit Yingcharoenrat
  • Victor Godet
  • Victor Gorbenko
  • Victor Matveev
  • Vsevolod Chestnov
  • Wanli Ju
  • Wei Li
  • Wei Xue
  • Wei-Ming Chen
  • Wojciech Zakrzewski
  • Xiang Zhao
  • Yang An
  • Yining You
  • Yixuan Li
  • Yue-Zhou Li
  • Yuta Hamada
  • Zahra Zahraee
  • Zheng-Quan Cui
  • Zhengwen Liu
  • Zhewei Yin
    • 2:30 PM 3:10 PM
      Positivity without Boosts: UV/IR Relations for Cosmology 40m

      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
    • 3:30 PM 4:10 PM
      A Timeless History of Time 40m

      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)
    • 4:30 PM 5:10 PM
      On analytic properties of cosmological correlators 40m
      Speaker: Viktor Gorbenko
    • 5:30 PM 6:00 PM
      Discussion 30m
      Speaker: Claudia de Rham (Imperial College London)
    • 2:30 PM 3:10 PM
      Positivity bounds in SMEFT and the inverse problem. 40m
      Speaker: Cen Zhang (Institute of High Energy Physics, Chinese Academy Sciences)
    • 3:30 PM 4:10 PM
      The facets of product moments: from EFThedron to Modularhedron 40m
      Speaker: yu-tin Huang
    • 4:30 PM 5:10 PM
      Positive Moments and Loops 40m
      Speaker: Francesco Riva
    • 5:30 PM 6:00 PM
      Discussion 30m
      Speaker: Joao Miguel Augusto Penedones Fernandes (EPFL - Ecole Polytechnique Federale Lausanne (CH))
    • 2:30 PM 3:10 PM
      Rigorous bounds on the analytic S-matrix 40m

      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
    • 3:30 PM 4:10 PM
      Celestial amplitudes: from UV constraints to conformal blocks 40m

      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
    • 4:30 PM 5:10 PM
      Positive sum rules in gravitational EFTs 40m

      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
    • 5:30 PM 6:00 PM
      Discussion 30m
      Speaker: Andrew Tolley (Imperial College London)