⇤Math diary
May 4, 2023:
Today I started trying to understand the Chiral De-Rahm complex. I find the original paper very hard to parse, because I don’t understand vertex algebras. To me, it looks like a soup of algebraic structures. skimmed through parts the paper Elliptic Genera and Applications to Mirror Symmetry, which looks more approachable for me. There is also the physics perspective in Chiral de Rham complex and the half-twisted sigma-model, which includes a Dolbeaut resolution of the Chiral De Rahm complex – more research needed.
Regardless, right now I’m trying to get a flavor for the Chiral De Rahm complex. Its clear that, if I want to really understand this, I have to go back and finally learn conformal field theory and vertex algebras. Which will take a while. I quite like parts of the book A mathematical introduction to CFT by Schottenloher, I think its time to go back and read the whole thing.