Week 05.02.2023 – 11.02.2023

These lectures aim to provide a self-contained introduction to the modern conformal bootstrap method. The study of conformal field theory (CFT) will first be motivated and the “old” way of studying CFTs as endpoints of RG flows will be explained. The set of ideas necessary to understand the conformal bootstrap method will then be introduced, and both analytic and numerical implementations of the conformal bootstrap method will be discussed.

In this talk, I will discuss the dynamical consequences of having 1-form and 2-group symmetries in Argyres-Douglas (AD) theories, particularly focusing on D_p(G) theories. I will first review how to construct (G,G') and D_p(G) theories from geometric engineering. Then, I will briefly review how 1-form symmetries are found in these AD theories, focusing on their dynamical consequences in the study of the Higgs branch for such theories. Analogously, I will show how certain D_p(G) theories enjoy a 2-group structure due to a non-trivial extension between a discrete 1-form symmetry and a continuous 0-form symmetry, emphasizing the dynamical consequences that a 2-group structure entails, and the family of AD theories that have it. If time permits it, I will show that it is possible to obtain an infinite family of AD theories starting from an arbitrary D_p(G) theory, where the theories in the same family share some properties. We called this "bootstrapping" of D_p(G) theories. The bootstrapping is also visible at the level of the 3d mirror theories of the D_p(G). My results are based mainly on arXiv:2203.16550 [hep-th] and arXiv:2208.11130 [hep-th].

In this talk I will develop Rafael D. Sorkin’s heuristic that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity can provide an objective physical correlate of our perception of time passing. I will argue that one cannot have an external, fully objective picture of the birth process because the order in which the spacetime atoms are born is a partial order. I propose that live experience in causal set theory is an internal “view” of the objective birth process in which events that are neural correlates of consciousness occur. In causal set theory, what “breathes fire” into a neural correlate of consciousness is that which breathes fire into the whole universe: the unceasing, partially ordered process of the birth of spacetime atoms.

Nonintegrable QFTs are expected to thermalize and exhibit emergence of hydrodynamics and chaos. In weakly coupled QFTs, kinetic theory captures local thermalization; such a versatile tool is absent away from the perturbative regime. I will present analytical and numerical results using nonperturbative methods to study thermalization at strong coupling. I will show how requiring causality in the thermal state leads to strong analytic constraints on the thermodynamics and out-of-equilibrium properties of any relativistic 1+1d QFT. I will then discuss Lightcone Conformal Truncation (LCT) as a powerful numerical tool to study thermalization of QFTs. Applied to \phi^4 theory in 1+1d, LCT reveals eigenstate thermalization and onset of random matrix universality at any nonzero coupling. Finally, I will discuss prospects for observing the emergence of hydrodynamics in QFTs using Hamiltonian truncation. (Based on: https://arxiv.org/abs/2207.11261 and https://arxiv.org/abs/2105.02229).

In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will review this connection for scattering amplitudes. After a broad review of the main ingredients involved, I will focus on maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory -- the momentum amplituhedron. In particular, I will show how such geometry encodes the properties of amplitudes. Finally, I will discuss some of the questions which remain open in this framework.