K3 metrics

Understand

We provide an explicit construction of Ricci-flat K3 metrics.

• It employs the technology of D-geometry, which in the case of interest is equivalent to a hyper-K\"ahler quotient.
• We relate it to the construction of arXiv:1810.10540, and in particular show that it contains the solution to the BPS state counting problem (that of computing the BPS index of a heterotic little string theory compactified on $T^2$) discussed therein, which is the data needed for this second construction of K3 metrics.