On integration over the supermoduli space of curved. A joint work with with Giovanni Felder and Alexander Polishchuk

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• David Kazhdan (Hebrew University of Jerusalem)
• Thursday 25 August 2022, 09:00-10:00
• Seminar Room 1, Newton Institute.

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NC2W02 - Crossing the bridge: New connections in number theory and physics

The partition function in perturbative Superstring Theory is presented as a series PgIgg where Ig =RSgµg is the integral over the supermoduli space Sg of supercurves of genus g, where µg is a supermeasure on Sg coming from the holomorphic Mumford’s form. The supermeasure µg is known to be continuous only for g ≤ 11 but even in this range there is a difficulty with a rigorous definition of the integral RSg µg. The main problem comes from the existence of the second order pole of the measure µg at the divisor at ∞. By choosing a cutofffunction ρ one can define the regularized integral Ig(ρ) but apriori it depends on a choice of a cutoff function. In the case when g = 2 we define a class C of cutoff functions ρ such that I2(ρ) does not depend on a choice of ρ ∈ C.

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