Week 07.11.2022 – 12.11.2022

The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes. The aim of these lectures is to introduce these ideas to a beginning PhD student in high energy physics.

The lectures will cover the following topics in succession:
- A review of the basics of black hole thermodynamics
- The ideas underlying the counting of statistical entropy of black holes in string theory
- The appearance of a special class of black holes called BPS black holes for which the statistical entropy can be calculated
- The nature of the corresponding microscopic ensemble of BPS states
- An illustration of the calculation of their statistical entropy in some simple examples.
At the end of these lectures, the student is meant to have gained an orientation with respect to the basic ideas and be equipped with some basic techniques used in microstate counting.

The defect CFT formed by inserting local operators along the supersymmetric Wilson line in N=4 SYM has received a lot of attention recently, and many new results have appeared at weak and strong coupling from a variety of techniques. In this talk I am going to focus on multipoint correlators in the weak-coupling regime, for which we derived a diagrammatic recursion relation that encompasses protected as well non-protected scalar fields. From this pool of results we conjectured new superconformal Ward identities that are believed to hold non-perturbatively. I will sketch how these identities can be used as the starting point for a strong-coupling analysis and discuss connections to other techniques.

The holographic principle posits a radical way to quantify gravitational physics. It claims that all information of a gravitational theory in a region of space can be encoded by a quantum theory at the boundary of this region. During this colloquium, I will discuss holography from an engineering perspective. We will see how one can engineer—i.e., design and build—gravity through this relationship, using possible quantum theories on the boundary as materials for the undertaking. The concrete advances will be presented for AdS_3/CFT_2: an instance of holography that relates three-dimensional gravity with a negative cosmological constant (AdS_3) to a two-dimensional conformal field theory (CFT_2).

The idea of the conformal bootstrap is to constrain observables through symmetries, consistency and a minimal amount of physical input. Using this method, correlators of insertions on one-dimensional defects in holographic setups are particularly apt to be computed. In this journal club, I will revisit the analytic bootstrap of the paper arXiv:2004.07849 and explore the three types of constraints listed above (symmetries, consistency and physical input) and how much information can be obtained through the conformal bootstrap. I will start by presenting the idea of the conformal bootstrap and introducing the holographic defect at play, I will then explicitly bootstrap the 1st-order 4-point correlator as an example of the method. In the final section, I will present some roadblocks as well as the additional inputs that have allowed higher orders to be computed (in a paper to appear), and how more restrictive constraints may yet be uncovered.