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.

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.

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.

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.

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.

Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. The agreement with experiments is good in many cases, e.g. the 3D Ising model, but disagreements between theory and experiment that have remained unresolved for decades also exist. This indicates that our understanding of critical phenomena may be incomplete. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of CFTs. In this talk we will review the numerical conformal bootstrap method and discuss potential resolutions it has suggested for unsettled questions pertaining to critical phenomena in frustrated magnets and structural phase transitions. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of unitary CFTs. In this talk we will review the numerical conformal bootstrap method and discuss its applications to 3D CFTs relevant for continuous phase transitions observed in various experiments.