Notes on She eld's quantum zipper

These are reading notes of She eld's Conformal welding of random surfaces: SLE and the quantum gravity zipper [11]. In that paper, She eld constructs a stationary process (ht, ηt)t∈R whose marginal law is given by a Gaussian free eld and an independent SLE curve. This process evolves with a deterministic cutting and unzipping dynamics: the curve is progressively unzipped, and the eld varies according to a natural change of coordinates. The main result of [11] is to prove that the process in reverse time (h−t, η−t)t∈R also evolves deterministically. In these notes, we go through She eld's proof of this result, with a minor variation in certain formulations using an idea of [2]. Let us also point to [3, Section 4] for other reading notes on the same topic.