Our mini-course lecturers this year will be John McGreevy (week 1), Ian Moult (week 2) and Henry Lin (week 3).

Entanglement Bootstrap [John McGreevy]

I plan to give an introduction to a perspective on states of matter and quantum field theory called Entanglement Bootstrap. The main idea is that all the universal information about a state of matter is encoded in the reduced density matrix of a ball of a representative state. We first apply this idea to understand liquid topological phases. Then we discuss extensions of this perspective to 1+1d conformal field theory groundstates, from which we can understand the emergence of conformal invariance from a single quantum state, and develop a strategy for an unbiased search for conformal field theories. If time allows, we will also talk about gapless edge modes of 2+1d topological phases, and conformal field theory in general dimensions.

Energy operators in Particle Physics, QFT, and Gravity [Ian Moult]

Detector operators, of which the average null energy operator provides the most famous example, arise as direct theoretical models of asymptotic measurements in collider experiments. In QFT, detector operators are expressed in terms of “light-ray operators”, whose correlation functions provide an interesting class of non-perturbatively well-defined observables.

There has recently been renewed interest in detector operators coming from three distinct directions: In CFTs, there has been progress understanding the space of light-ray operators, their organization into Regge trajectories, and their appearance in Lorentzian operator product expansions. In perturbative QFT and gravity, borrowing techniques from the study of scattering amplitudes, there has been progress understanding multi-point correlation functions of detector operators, in particular, their function space and singularities. Finally, in particle physics, there have recently been direct measurements of correlation functions of detector operators in collider experiments, enabling measurements of their scaling behavior and the structure of multi-point correlators of light-ray operators in QCD.

In this mini-course I will give an introduction to the theory of light-ray/ detector operators, their correlators, and their applications in particle phenomenology, and provide an overview of the recent progress in the directions mentioned above. Throughout, I will attempt to highlight the different perspectives and motivations for studying these operators, coming from the CFT, amplitudes and phenomenological communities.

I will conclude with a discussion of open problems in both theory and phenomenological applications, as well as highlighting areas where theoretical developments could have an impact on real world applications at colliders.

Bootstrapping matrix quantum mechanics [Henry Lin]

In these lectures, we will review recent advances in bootstrapping quantum mechanical systems with matrix degrees of freedom, including the BFSS matrix model in the large N limit. We will discuss numerical bootstrap methods for constraining vacuum expectation values, thermodynamics, and time dependent 2-pt functions. We will discuss prospects for learning about stringy corrections to black hole physics using the bootstrap.