I recently discovered about Minhyong Kim's work on what can be coined "Arithmetic Gauge Theory/Arithmetic Chern Simmons Theory". Since Liouville quantum gravity is fully understood, I was wondering if there would be some intersections and potential usefulness of studying algebraic curves using 2d conformal field theories.
Remark: I have just graduate student base knowledge and I'm not an expert on any of these areas. So I apologise in advance for the vagueness and possibly ill-formed question, but I am just curious and don't really know where else to ask.
