Appears in collection : Korea-France Joint Workshop on String Theory

I will review recent developments in extending the bulk–boundary correspondence between three-dimensional topological quantum field theories (TQFTs) and two-dimensional rational conformal field theories (RCFTs) to the non-unitary setting. This correspondence can be viewed as a generalization of the celebrated Chern–Simons/Wess–Zumino–Witten (CS/WZW) correspondence. Remarkably, the corresponding bulk TQFTs can be physically realized as topological twists of an exotic class of three-dimensional N=4 superconformal field theories known as rank-zero SCFTs. I will present several non-trivial dictionaries of the correspondence and describe their verification through concrete examples. I will also discuss mathematical and physical applications of this non-unitary bulk–boundary correspondence.