This is the third talk of 2024 in the Western Hemisphere Colloquium on Geometry and Physics. See web.math.ucsb.edu/~drm/WHCGP/ for more information on this series and to sign up to receive Zoom links for future talks.
Abstract: A holomorphic quantum field theory is one which is sensitive to the complex structure of spacetime; in complex dimension one this is simply a (chiral) conformal field theory. I will give examples of holomorphic QFTs which exist in higher dimensions, some of which appear within the context of supersymmetry. I will then survey recent approaches to a rigorous axiomatization of holomorphic quantum field theory which build off of well-combed methods in CFT, such as the theory of vertex algebras. Finally, I will highlight some open problems in holomorphic QFT as well as applications to the understanding of the ubiquitous six-dimensional superconformal field theory.