Plan of the talk
In order to prove the descent procedure, we will need two ingredients:

  1. Relation between the cohomology of and the Lie algebra cohomology.

    Lie algebra cohomology is the cohomology of the operator which is well-known to physicists:

    This is what is usually called “BRST operator” e.g. in Yang-Mills theory. But mathematicians call such things “Lie algebra cohomology”. It turns out that the BRST cohomology can be cast in this form.

  2. Some observation about the integrable structure of the worldsheet theory