Title:
String Measure on the Genus Zero Supermoduli Space
Abstract:
Partition functions and scattering amplitudes in superstring theory are fundamental quantities, computed as integrals over the moduli spaces $mathcal{M}{g,n{mathrm{NS}},n_{mathrm{R}}}$ of super Riemann surfaces of genus $g$ with Neveu–Schwarz (NS) and Ramond (R) punctures with respect to a certain measure. These quantities admit expansions in powers of $hbar^g$, with low genus contributions playing a dominant role.In this talk, I will present a computation of the genus-zero superstring measure on the moduli space of genus zero super Riemann surfaces with Neveu–Schwarz punctures. While the resulting measure has long been known to physicists, our approach derives it from first principles, using only complex algebraic supergeometry and, in particular, the super Mumford isomorphism.Time permitting, I will discuss the Ramond case, where the corresponding string measure is expected to be genuinely new; this work is currently in progress. This is joint work with S. Cacciatori and S. Grushevsky: the NS case is published, and the Ramond case is ongoing.
Bio:
Alexander Voronov received his Ph.D. in Mathematics from Moscow State University under the supervision of Yuri I. Manin. Voronov has held positions at Princeton University, MIT, and the University of Pennsylvania, and since 2001 has been a faculty member at the University of Minnesota. He is also affiliated with the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU).
Voronov is known for the construction of the super Mumford isomorphism, for foundational work on semi infinite homological algebra, for introducing a real version of the Deligne–Mumford compactification, and for defining the Swiss cheese and cactus operads, which play important roles in higher algebra and string topology. He has given proofs of conjectures of Deligne and Kontsevich on Hochschild cohomology and discovered Mysterious Triality linking geometry, topology, and mathematical physics