2D rational conformal field theories (RCFTs) are typically thought of as being the “nicest” interesting CFTs we can study: They have large enough symmetry so that there are only a finite number of primary fields, but they also have applications to the real world (e.g., to various condensed matter systems). In this talk, I will describe a program that aims to understand connections between exotic 4D theories with N=2 superconformal symmetry and more down-to-earth 2D RCFTs, thereby enriching our understanding of both.

In the first part of the talk, I will revisit the question of how to decide whether two 4D N=2 superconformal field theories describe the same physics. Time permitting, I will discuss related questions regarding the classification of 2D rational conformal field theories.

Lecture 3: "Toward a Synthesis of Chiral Rings and Chiral Algebras." I will aim to discuss some recent work that seeks to relate the objects introduced in the first two lectures. Given enough time, we may also discuss generalizations of these ideas.

Lecture 2: "Chiral Algebras and Higher-Dimensional Theories." I will review briefly review the construction of chiral algebras and then focus on their relationship with a particular sub-sector of operators in higher-dimensional theories. I will again focus mostly on 4D N=2 theories.

Lecture 1: "Chiral Rings, Moduli Spaces, and Conformal Manifolds." In this lecture I will review basic aspects of chiral operators, with a special focus on 4D theories with 8 Poincare supercharges (i.e., N=2 SUSY). Using these operators, I will discuss basic aspects of moduli spaces and conformal manifolds.

We will show that a large class of N=2 SUSY field theories do not have SUSY breaking vacua.