The Super Period Matrix with Ramond Punctures in the supergravity formulation

Understand

In a very recent preprint, Witten showed how to construct a $g|r \, \times \, g|r$ super period matrix for super Riemann surfaces of genus $g$ with $2r$ Ramond punctures, which is symmetric in the ${\bf Z}_2$ graded sense.

• He also showed how it can be applied to analyze supersymmetry breaking in string compactifications which are supersymmetric at tree-level.
• Witten's construction is in the purely holomorphic formulation of super Riemann surfaces.
• In this paper, a construction is given in the formulation of two-dimensional supergravity.