In a paper published ten years ago, we introduced an invariant of K3 surfaces with involution, which we constructed using equivariant analytic torsion, and we proved its automorphic property.

In this talk, after explaining the physical origin of the invariant, we will give its structure theorem: it is the tensor product of an explicit Borcherds product and an explicit Siegel modular form, possibly except two cases. This is a joint work with Shouhei Ma.