O(N) x O(2) model from 3D to 4D - the tale of disappearing fixed points

• Slava Rychkov (IHES, Bures-sur-Yvette)

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.

Twist-4 trajectories and missing local operators

• Johan Henriksson (IPhT, Saclay)

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.

Taming Mass Gap with Anti-de Sitter Space

• Lorenzo Di Pietro (University of Trieste)

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.

Bootstrap and experiments in condensed matter and particle physics

• Ning Su (Caltech)

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.

Gradient Properties of RG Flows

• Andreas Stergiou (King's College London)

Thermal one-point blocks

• Francesco Russo (University of Pisa)

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.

T\bar T and J\bar T - deformed CFTs: symmetries, correlators and generalisations

• Monica Guica (CERN)

Revisiting Lattice and Matrix Bootstrap

• Zechuan Zheng (Perimeter Institute)

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.

Finding fixed points in the epsilon expansion

• Hugh Osborn (Cambridge University)

Improving the Five-Point Bootstrap

• David Poland (Yale University)

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.

Advancing the Multipoint Bootstrap

• Volker Schomerus (DESY)

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.

Bootstrapping Mesons at large N

• Leonardo Rastelli (Stony Brook University)

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

Trace anomalies and the dilation-graviton amplitude

• Denis Karateev (University of Geneva)

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.

Bootstrapping N = 4 SYM for all N and coupling

• Shai Chester (Imperial College London)

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.

Bounds on QCD observables: hadronic strings, glueball scattering, and meson spectrum

• Andrea Guerrieri (Perimeter Institute and University of Padova)

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.

A new twist on spin

• Guilherme Pimentel (Scuola Normale Superiore)

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.

Positivty bounds on massive vectors

• Francesco Bertucci (University of Pisa)

Fuzzy Sphere regularization of 3D CFTs: A recent progress

• Yin-Chen He (Perimeter Institute)

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.

Bootstrapping gauge theories

• Yifei He (École normale supérieure)

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.

Numerical bootstrap for points and lines

• Marco Meineri (University of Torino)

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.

Bootstrapping Boundary QED

• Christopher Herzog (King's College London)

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.

Advanced Non-Perturbative Techniques in N=4 SYM Theory

• Nikolay Gromov (King's College London)

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.

Multi-trace operators in CFTs

• Agnese Bissi (ICTP Trieste)

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.

AdS three-body problem at large spin

• Jeremy Mann (King's College London)

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.

Gravity from quantum mechanics of finite matrices

• Xiang Zhao (EPFL)

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.