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