Below is the list of confirmed speakers. Further speakers will be announced in the next few days. We expect all talks to be recorded.
Gabriel Cuomo (SCGP): The large charge sector of CFTs
I will review some recent progress in analyzing the spectrum of operators carrying a large internal charge in Conformal Field Theories (CFTs). The large charge sector of CFTs can be generically studied semiclassically in an expansion in inverse powers of the charge. I will first present the basic construction discussing the calculation of the scaling dimension of the lowest dimensional operator with large charge for the U(1) Wilson-Fisher fixed point in the epsilon expansion. This result will be used to introduce a general effective theory description of large charge operators in terms of a single superfluid Goldstone boson. I will then use effective field theory to study operators with both large charge and large spin in 3d CFTs, extending some previous analyses and providing results complementary to the bootstrap predictions for large spin multi-trace operators. If time permits, I will also briefly review the generalization of this analysis for theories with moduli spaces.
Mert Besken (Amsterdam): Virasoro conformal bootstrap with c > 1
We derive new constraints on the spectrum of two-dimensional conformal field theories with central charge c>1. Employing the pillow representation of the four point correlator of identical scalars with dimension Delta_O and positivity of the coefficients of its expansion in the elliptic nome we place central charge dependent bounds on the dimension of the first excited Virasoro primary the scalar couples to, in the form Delta_1 < f(c,Delta_O). We give an analytic expression for f(c,Delta_O) and write down transcendental equations that significantly improve the analytic bound. We numerically evaluate the stronger bounds for arbitrary fixed values of c and Delta_O.
Yin-Chen He (Perimeter): A roadmap for bootstrapping critical gauge theories
Solving critical gauge theories with conformal bootstrap remains an open problem. In this talk I will introduce our recent progress on bootstrapping critical gauge theories. In particular, I will provide a simple and workable answer to the question of how to detect the gauge group in the bootstrap calculation. Our proposal is based on the notion of decoupling operator, which can be viewed as the higher dimensional reminiscent of null operators of 2d Wess-Zumino-Witten CFTs. As an application we study a prototypical critical gauge theory--the scalar QED theory, i.e., critical bosons interacting with a U(1) gauge field. I will show that the scalar QED can be solved by conformal bootstrap, namely we have obtained its kinks and islands in both d=3 and d=2+epsilon dimensions.
Walter Landry (Caltech): Outer Approximation, Approximate Objectives, and Enhancements to SDPB
I will briefly go over the latest enhancements to SDPB, followed by details about two new tools. The first is Approx_Objective, which quickly approximates the objective of a semidefinite program (SDP) given a solution to a nearby SDP. The other is Outer_Limits, an experimental new SDP solver that uses the outer approximation. One practical difference from SDPB is that Outer_Limits can be applied to problems without requiring a polynomial approximation. It also allows Outer_Limits to solve SDPs with dramatically smaller requirements on numerical precision.
Madalena Lemos (Durham): Regge trajectories for the (2,0) theories
We investigate the structure of conformal Regge trajectories for the maximally supersymmetric (2,0) theories in six dimensions. The different conformal multiplets in a single superconformal multiplet must all have similarly-shaped Regge trajectories. We show that these super-descendant trajectories interact in interesting ways, leading to new constraints on their shape. For the four-point function of the stress tensor multiplet supersymmetry also softens the Regge behavior in some channels, and consequently we observe that 'analyticity in spin' holds for all spins greater than -3. All the physical operators in this correlator therefore lie on Regge trajectories and we describe an iterative scheme where the Lorentzian inversion formula can be used to bootstrap the four-point function. Some numerical experiments yield promising results, with OPE data approaching the numerical bootstrap results for all theories with rank greater than one.
Miguel Paulos (ENS): Mastering bounds on correlators
We discuss a new viewpoint onto the CFT landscape: bounds on values of CFT correlators. We show that such bounds can be obtained by constructing suitable 'master functionals'. We present both numerical results for 3d CFTs as well as exact results for correlators on the line. The latter follow from crossing symmetric dispersion relations. We briefly discuss how these may be used to study the Regge and flat space limits of CFT correlators.
Joao Penedones (EPFL) and Lorenzo Di Pietro (Trieste): Gauge theory fixed points in 5D (discussion session)
Eric Perlmutter (IPHT Saclay): On The Structure of 2D CFT Spectra
I will explain how the spectra of 2D CFTs, rational and irrational, exhibit surprising rigidity and determinacy. This hidden structure follows from leveraging discreteness, integrality and modularity constraints in new ways. Our techniques suggest alternative analytic bootstrap approaches to the space of 2D CFTs.
David Simmons-Duffin (Caltech): AdS Bulk Locality from Sharp CFT Bounds