The super period matrix with Ramond punctures

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We generalize the super period matrix of a super Riemann surface to the case that Ramond punctures are present. For a super Riemann surface of genus g with 2. r Ramond punctures, we define, modulo certain choices that generalize those in the classical theory (and assuming a certain generic condition is satisfied), a g. r× g. r period matrix that is symmetric in the Z2-graded sense. As an application, we analyze the genus 2 vacuum amplitude in string theory compactifications to four dimensions that are supersymmetric at tree level. We find an explanation for a result that has been found in orbifold examples in explicit computations by D'Hoker and Phong: with their integration procedure, the genus 2 vacuum amplitude always vanishes "pointwise" after summing over spin structures, and hence is given entirely by a boundary contribution.

Original languageEnglish (US)
Pages (from-to)210-239
Number of pages30
JournalJournal of Geometry and Physics
StatePublished - Jun 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology


  • Algebraic geometry
  • Strings and superstrings
  • Supermanifolds and supergroups


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