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Seminar

22.06.2022   at 15:00 - 16:00

QM Research Seminar by Nadia Ott (Univ. Pennsylvania): Super period matrix with Ramond punctures - Description of bad locus

Super Riemann surfaces and their moduli spaces Mg are supersymmetric generalizations of the classical notions of Riemann surfaces. In physics, super Riemann surfaces are the worldsheets of propagating superstrings and once can define important quantities in superstring theory, e.g., vacuum and scattering amplitudes, as integrals over Mg. These integrals are measured according to a certain volume form on Mg defined using the generalization of the usual period map to the super case. It turns out that in the super case the period map is only defined away from the vanishing thetanulls in the ordinary moduli space of curve Mg. One can describe the vanishing thetanull divisor as the locus of curves C in Mg supporting an even spin structure L such that h (L) ≥ 2. There exists an analog of the period matrix for certain super Riemann surfaces with Ramond punctures. It was previously not known how to describe the locus (called the “bad locus”) in the moduli space Mg,2r of genus g super Riemann surfaces with 2r Ramond punctures along which this super period matrix is not defined. In joint work with Ron Donagi, we described this locus explicitly in terms of the generalized spin structure L as those curves supporting a generalized spin structure L such that h0 (L) > r. Furthermore, we expect that the associated period map on Mg,2r can be used to define a volume form on Mg,2r which generalizes the volume form on Mg used to compute the g-superstring vacuum amplitude.