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SUMMARY:On integration over the supermoduli space of curved. A joint work 
 with with Giovanni Felder and Alexander Polishchuk - David Kazhdan (Hebrew
  University of Jerusalem)
DTSTART:20220825T080000Z
DTEND:20220825T090000Z
UID:TALK177236@talks.cam.ac.uk
DESCRIPTION:The partition function in perturbative Superstring Theory is p
 resented as a series PgIgg where Ig =RSg&micro\;g is the integral over the
  supermoduli space Sg of supercurves of genus g\, where &micro\;g is a sup
 ermeasure on Sg coming from the holomorphic Mumford&rsquo\;s form. The sup
 ermeasure &micro\;g is known to be continuous only for g &le\; 11 but eve
 n in this range there is a difficulty with a rigorous definition of the in
 tegral RSg &micro\;g. The main problem comes from the existence of the sec
 ond order pole of the measure &micro\;g at the divisor at &infin\;. By cho
 osing a cutofffunction &rho\; one can define the regularized integral Ig(&
 rho\;) but apriori it depends on a choice of a cutoff function. In the cas
 e when g = 2 we define a class C of cutoff functions &rho\; such that I2(&
 rho\;) does not depend on a choice of &rho\; &isin\; C.
LOCATION:Seminar Room 1\, Newton Institute
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