This course will provide a modern point of view on the wide world of large $N$ conformal field theory (CFT) in diverse spacetime dimensions, placed in the context of the conformal bootstrap and the AdS/CFT Correspondence.

Some questions we will tackle:

• What is a ``Holographic CFT''?
• When does a CFT give rise to an equivalent, emergent simple gravity description?
• What is the conformal bootstrap, and how is it used to constrain and classify the space of consistent large $N$ CFTs and theories of quantum gravity?
• Is string theory the only choice? How can we detect strings and extra dimensions from properties of field theories?
• What precise predictions does quantum gravity seem to make about the space of strongly coupled CFTs?

Provisional lecture plan:

Lectures I-II: Introducing CFTs and their data, large $N$ conformal bootstrap, AdS/CFT, and the notion of ``Holographic CFT''

Lecture III: Correlation functions and holography

Lecture IV: Bootstrapping the space of Holographic CFTs

Lecture V: Special focus: Two-dimensional CFTs and AdS$_3$ gravity