50 + ε Years of Conformal Bootstrap

19 Feb 2024, 08:00 → 23 Feb 2024, 19:00 Europe/Rome

 

In celebration of 50 + ε years of the conformal bootstrap, the Conformal Field Theory group at the University of Pisa and INFN Pisa is holding a conference on bootstrap approaches to quantum field theory and related topics.

Speakers:

Agnese Bissi               Uppsala and ICTP Trieste 

Andrea Guerrieri         Perimeter Institute and University of Padova

Andreas Stergiou        King's College London

Christopher Herzog    King's College London

David Poland               Yale

Denis Karateev            University of Geneva

Francesco Bertucci     University of Pisa and INFN Pisa

Francesco Russo        University of Pisa and INFN Pisa

Gui Pimentel                SNS Pisa

Hugh Osborn               Cambridge

Johan Henriksson      IPhT, Saclay

Leonardo Rastelli        SUNY, Stony Brook

Lorenzo Di Pietro        University of Trieste

Marco Meineri             University of Torino

Monica Guica              IPhT, Saclay and CERN and EPFL

Nikolay Gromov          King's College London

Ning Su                        Caltech and MIT

Petr Kravchuk             King's College London

Shai Chester               Imperial College London

Slava Rychkov            IHES

Volker Schomerus     DESY

Xiang Zhao                  EPFL

Yifei He                        ENS, Paris

Yin-Chen He                Perimeter Institute

Zechuan Zheng          Perimeter Institute

 

 

The organizers:

Alessandro Vichi, alessandro.vichi@unipi.it

Ilija Buric, ilija.buric@df.unipi.it 

Laura Engelbrecht, laura.engelbrecht@df.unipi.it

Stefanos Robert Kousvos, stefanos.kousvos@df.unipi.it

Don't hesitate to contact us with any inquiry regarding the conference.

Monday, 19 February

09:00 → 10:00 O(N) x O(2) model from 3D to 4D - the tale of disappearing fixed points

O(N) x O(2) model furnishes an example of a system where unitary fixed points exist in a range of N above some N_c(d), where N_c(d) is a rapidly varying function. I will describe how N_c(d) can be found using the conformal bootstrap. Joint work with Marten Reehorst, Balt van Rees, and Benoit Sirois.

Speaker: Slava Rychkov (IHES, Bures-sur-Yvette)

2024-Pisa-Rychkov.pdf

11:00 → 11:45 Twist-4 trajectories and missing local operators

In this talk, I will discuss the structure of spinning operators in
CFTs. Specifically, there is a tension between the idea that all
spinning operators belong to Regge trajectories with data analytic in
spin, and the fact that the number of local operators below a given
twist grows with spin. This means that Regge trajectories, suitably
defined through light-ray operators, must decouple from all local
correlation functions at the spins where local operators are missing,
requiring infinitely many conditions for a single trajectory. I will
explain how to resolve this tension by demonstrating that the
vanishing conditions in all correlators follow from a single condition
related to the normalisation of the light-ray operator. This will be
illustrated by considering the Wilson-Fisher fixed point, where we can
explicitly construct the light-ray operators of twist-4 trajectories
at complex spin, and directly observe the vanishing conditions at low
integer spin.

Speaker: Johan Henriksson (IPhT, Saclay)

Henriksson-Pisa-final.pdf

12:00 → 12:45 Taming Mass Gap with Anti-de Sitter Space

Anti-de-Sitter space acts as an infra-red cutoff for asymptotically free theories, allowing interpolation between a weakly-coupled small-sized regime and a strongly-coupled flat-space regime. I will discuss this interpolation for theories in two dimensions from the perspective of boundary conformal theories. The appearance of a singlet marginal operator destabilizes a gapless phase existing at a small size, triggering a boundary renormalization group flow to a gapped phase that smoothly connects to flat space.

Speaker: Lorenzo Di Pietro (University of Trieste)

SeminarPisa2024.pdf

14:30 → 15:30 Bootstrap and experiments in condensed matter and particle physics

The bootstrap method explores fundamental consistency conditions to constrain physical observations. These consistency conditions often translate into highly non-trivial numerical problems. The application of the bootstrap method in physics crucially depends on advancements in numerical techniques. In this talk, I will review recent developments in bootstrap numerics, and show that, with advanced numerics, formal constraints such as unitarity and crossing symmetries lead to precise predictions for experimental phenomena in condensed matter and high energy physics.

Speaker: Ning Su (Caltech)

Pisa.pdf

16:30 → 17:30 Gradient Properties of RG Flows

Speaker: Andreas Stergiou (King's College London)

Andy-Gradient_RG_flows.pdf

17:30 → 18:00 Thermal one-point blocks

We compute one-point blocks in thermal Conformal Field Theories on S^1 \times S^{d-1}. Specifically, we derive the Casimir for spinning representations and solve it with an ansatz. Potential applications to (holographic) correlators will also be discussed.

Speaker: Francesco Russo (University of Pisa)

Pisa_Conference__24-2 (1).pdf

Tuesday, 20 February

09:00 → 10:00 T\bar T and J\bar T - deformed CFTs: symmetries, correlators and generalisations

Speaker: Monica Guica (CERN)

ttb_jtb_symm_pisa.pdf

11:00 → 11:45 Revisiting Lattice and Matrix Bootstrap

This presentation focuses on the lattice and matrix bootstrap methods, distinguished by their utilization of the equation of motion as bootstrap constraints. These methods share key characteristics with the closely related fields of quantum mechanics bootstrap and many-body bootstrap. I will discuss the latest results in bootstrap finite N lattice gauge theory, including the calculation of string tension through the bootstrap approach. Additionally, the presentation will cover the application of the relaxation method to the bootstrap of matrix quantum mechanics (MQM), with a particular emphasis on the ground state of MQM.

Speaker: Zechuan Zheng (Perimeter Institute)

Zheng.pdf

12:00 → 12:45 Finding fixed points in the epsilon expansion

Speaker: Hugh Osborn (Cambridge University)

Osborn.pdf

14:30 → 15:30 Improving the Five-Point Bootstrap

I'll describe an improved approach to computing conformal blocks and applying the conformal bootstrap to 5-point correlation functions, giving new results for OPE coefficients involving multiple spinning operators in the 3d Ising CFT.

Speaker: David Poland (Yale University)

Pisa-Poland-2-20-24.pdf

16:30 → 17:30 Advancing the Multipoint Bootstrap

Multipoint correlation functions of scalar operators provide access to new CFT data that
is invisible to scalar 4-point functions. Most importantly, they may be exploited to probe
multitwist operators. In this talk I shall survey some recent advances in both the
numerical and lightcone bootstrap for 6-point correlators, based on joint work with
A. Antunes, S. Harris, A. Kaviraj, J. Mann, L. Quintavalle.

Speaker: Volker Schomerus (DESY)

Bootstrapv2-2.pdf

Wednesday, 21 February

09:00 → 10:00 Bootstrapping Mesons at large N

I will review recent progress in constraining the meson sector of large N QCD from a modern bootstrap perspective

Speaker: Leonardo Rastelli (Stony Brook University)

PionsPIsa.pdf

11:00 → 11:45 Trace anomalies and the dilation-graviton amplitude

We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to (∆c − ∆a) along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate (∆c − ∆a) to spinning massive states in the spectrum of the QFT. We test our predictions on a simple example of a massive free scalar. We discuss possible applications.

Speaker: Denis Karateev (University of Geneva)

c-anomaly.pdf

12:00 → 12:45 Bootstrapping N = 4 SYM for all N and coupling

We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension operator in N = 4 SU( N) super-Yang-Mills theory for a wide range of N and Yang-Mills couplings g. We find that our bounds are approximately saturated by weak coupling results at small g. Furthermore, at large N our bounds interpolate between integrability results for the Konishi operator at small g and strong-coupling results, including the first few stringy corrections, for the lowest-dimension double-trace operator at large g. In particular, our scaling dimension bounds describe the level splitting between the single- and double-trace operators at intermediate coupling.

Speaker: Shai Chester (Imperial College London)

bootNew.pdf

14:30 → 15:30 Bounds on QCD observables: hadronic strings, glueball scattering, and meson spectrum

The numerical S-matrix Bootstrap establishes non-perturbative universal bounds on physical observables extracted from scattering amplitudes in any dimension.
Often, from a bound, it is possible to extract the extremal amplitudes and learn valuable lessons on non-perturbative physics.
In this talk, I will review some of the most recent applications of Bootstrap to QCD observables.
First, I will discuss the bounds on the quark-antiquark potential in 3d and 4d, and show how the QCD world-sheet axion emerges from the extremal amplitudes.
Next, I will focus on the bounds of coupling constants among SU(3) glueballs that rely only on rigorous properties of QFTs in four dimensions.
Finally, I will briefly show some preliminary results obtained by injecting the experimentally available data on \pi\pi scattering.
The goal is to start a precision physics program for hadronic physics based on bootstrap methods.

Speaker: Andrea Guerrieri (Perimeter Institute and University of Padova)

Bounds_on_QCD_Observables_2.pdf

16:30 → 17:30 A new twist on spin

I will describe new kinematic variables to describe correlation functions of conserved currents in CFTs. In these variables there is a tantalizing connection to scattering amplitudes in flat space. Work in progress with Daniel Baumann, Gregoire Mathys and Facundo Rost.

Speaker: Guilherme Pimentel (Scuola Normale Superiore)

Talk.pdf

17:30 → 18:00 Positivty bounds on massive vectors

Speaker: Francesco Bertucci (University of Pisa)

bertucci_pisaseminar.pdf

Thursday, 22 February

09:00 → 10:00 Fuzzy Sphere regularization of 3D CFTs: A recent progress

I will talk our recent progress in applying fuzzy sphere regularization to study 3D CFTs. After a brief introduction of the basic idea of fuzzy sphere regularization, I will then focus on its advanced applications, particularly, how to extract non-local universal information of CFTs such as the RG monotonic F-function as well as various properties of conformal defect.

Speaker: Yin-Chen He (Perimeter Institute)

fuzzy_Pisa_2.pdf

11:00 → 11:45 Bootstrapping gauge theories

We propose the Gauge Theory Bootstrap, a method to compute the pion S-matrix that describes the low energy physics of the strong interaction and other similar gauge theories. The phase shifts of the S0, P1, S2 waves obtained are in good agreement with experimental results. The only numerical inputs are the quark mass m_q, the QCD scale Lambda_QCD, the pion mass m_\pi and the pion decay constant f_\pi without any other experimental data. We make use of the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules.

Speaker: Yifei He (École normale supérieure)

Pisa_YifeiHE.pdf

12:00 → 12:45 Numerical bootstrap for points and lines

I will describe how to constrain the spectrum of local operators and boundary conditions, in two dimensions, using the numerical bootstrap. Crossing and unitarity constrain the correlators of four local operators, two local operators and a boundary, and two boundaries. This allows to explore a multi-dimensional parameter space involving bulk and boundary data: I will show a few examples of the bounds one can obtain.

Speaker: Marco Meineri (University of Torino)

14:30 → 15:30 Bootstrapping Boundary QED

There is a graphene-like boundary conformal field theory which consists of charged conformal degrees of freedom confined to a surface interacting with a photon in the bulk. A long introduction will develop several features of this theory: its relation to graphene and three dimensional QED; ways to introduce supersymmetry; its behavior under the action of SL(2,Z). Then I will talk about recent work describing our efforts to subject this theory to the numerical conformal bootstrap.

Speaker: Christopher Herzog (King's College London)

pisa2024.pdf

16:30 → 17:30 Advanced Non-Perturbative Techniques in N=4 SYM Theory

I will report on recent advances in Bootstrability -- a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N=4 SYM. We will discuss the method in applications to the 1D defect CFT. Integrability not only produces a spectrum in this theory but also provides information in the form of integrated correlators. Combining this information we obtain very sharp rigorous numerical bounds for the structure constant of the first non-protected states, giving this observable with seven digits precision for the 't Hooft coupling in the intermediate coupling region λ/√4π∼1, with the error decreasing quickly at large 't Hooft coupling.

We also studied the problem of bounding directly a 4-point function at generic cross ratio. Our numerical bounds give an accurate determination of the 4-point function for physical values of the cross ratio.

Speaker: Nikolay Gromov (King's College London)

2024 Pisa .pdf

Friday, 23 February

09:00 → 10:00 Multi-trace operators in CFTs

In this talk I will discuss how to deal with multi-trace operators, in particular in the context of N=4 Super Yang Mills. I will review their relevance in computing holographic correlators and discuss recent developments on how to treat them.

Speaker: Agnese Bissi (ICTP Trieste)

pisa 2024.pdf

11:00 → 11:45 AdS three-body problem at large spin

Motivated by the problem of understanding multi-twist operators in general CFTs, I will discuss the large-spin leading-twist three-particle states in AdS. In particular, I will explain that thanks to the AdS curvature this particular limit of the three-body problem is tractable. The large spin limit effectively becomes a semiclassical limit of a Berezin-Toeplitz Hamiltonian, which allows us to analyze the leading-twist spectrum analytically. Work in progress with Jeremy Mann.

Speaker: Jeremy Mann (King's College London)

ads_3body_v6.pdf

12:00 → 12:45 Gravity from quantum mechanics of finite matrices

In the first part I will briefly review the Banks-Fishcler-Shenker-Susskind (BFSS) and the Berenstein-Maldacena-Nastase (BMN) conjectures relating M-theory and Matrix Quantum Mechanics (MQM) of N × N matrices. In particular, I will differentiate between the weaker form (large N) and the stronger form (finite N) of the conjectures.

In the second part, I will focus on quantum mechanics. After explaining the techniques and subtleties of finding an effective description of a strongly coupled system, I will show that the BMN MQM at strong coupling and finite N describes non-relativistic free particles in a harmonic trap. The energy spectrum predicted by this Hamiltonian matches the supergravity excitation spectrum around the PP-wave background, if we further assume the existence of bound states.

Speaker: Xiang Zhao (EPFL)

[2024-02-23] Pisa_Zhao_PDF.pdf