Week 22.01.2023 – 28.01.2023

The epsilon-expansion was invented more than 50 years ago and has been used extensively ever since to study aspects of renormalization group flows and critical phenomena. Its most famous applications are found in theories involving scalar fields in (4-epsilon) dimensions. In this talk, we will discuss the structure of the epsilon-expansion and the fixed points that can be obtained within it. We will mostly focus on scalar theories, but we will also discuss theories with fermions as well as line defects. Our motivation is based on the goal of classifying conformal field theories in d=3 dimensions. We will describe recently discovered universal constraints obtained within the framework of the epsilon-expansion and show that a 'heavy handed' quest for fixed points yields a plethora of new ones. These fixed points reveal aspects of the structure of the epsilon-expansion and suggest that a classification of conformal field theories in d=3 is likely to be highly non-trivial.

We describe the dynamical evaporation of a black hole as the classical evolution in time of a black hole in an Anti-de Sitter braneworld. A bulk black hole whose horizon intersects the brane yields the classical bulk dual of a black hole coupled to quantum conformal fields. The evaporation of this black hole happens when the bulk horizon slides off the brane, making the horizon on the brane shrink. We use a large-D effective theory of the bulk Einstein equations to solve the time evolution of these systems. With this method, we study the dual evaporation of a variety of black holes interacting with colder radiation baths. We also obtain the dual of the collapse of holographic radiation to form a black hole on the brane.

I will discuss how to setup renormalization of bulk loops in AdS and the implications for the AdS/CFT correspondence.