TY - JOUR

T1 - The super period matrix with Ramond punctures

AU - Witten, Edward

N1 - Funding Information:
Research was partly supported by NSF Grant PHY-1314311 . I would like to thank E. D’Hoker, R. Donagi, and D. Phong for discussions, and D’Hoker and Phong for help in reconciling some formulas here with their results. I also thank P. Deligne for detailed comments on an earlier version and for several helpful suggestions.
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - 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.

AB - 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.

KW - Algebraic geometry

KW - Strings and superstrings

KW - Supermanifolds and supergroups

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U2 - 10.1016/j.geomphys.2015.02.017

DO - 10.1016/j.geomphys.2015.02.017

M3 - Review article

AN - SCOPUS:84924726149

SN - 0393-0440

VL - 92

SP - 210

EP - 239

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -