The super period matrix with Ramond punctures in the supergravity formulation

• Main Authors: Eric D'Hoker, Duong H. Phong
• Format: Article
• Language: English
• Published: Elsevier 2015-10-01
• Series: Nuclear Physics B
• Online Access: http://www.sciencedirect.com/science/article/pii/S0550321315002965

In a very recent preprint, Witten showed how to construct a g|r×g|r super period matrix for super Riemann surfaces of genus g with 2r Ramond punctures, which is symmetric in the Z2 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. The variations of the super period matrix with respect to supermoduli deformations are also given, as well as an explicit illustration of how the super period matrix with two Ramond punctures would emerge from a degeneration of the super period matrix without punctures in higher genus.