Working Seminar on Mathematical Physics of HSE University and Skoltech Krichever Center: Igor Fedorov (Skoltech, HSE Univ.)

Genus 3 superstring measure

 I am going to speak on the super Mumford form. It is a certain volume form on the moduli space of super Riemann surfaces of given genus, the ``holomorphic part'' of the superstring measure; the latter is analogous to the Polyakov measure for bosonic strings. To compute superstring scattering amplitudes, it is desirable to have explicit formulae for the super Mumford form; there are formulae for genus 1 and 2 via period matrices. No analogous formula for genus 3 is known (to be more precise, Cacciatori, Dalla Piazza & van Geemen proposed an ansatz in 2008, but in 2015 Witten argued that this ansatz is not suitable). I try to derive a formula for genus 3 for the "top component" of the super Mumford form; I have not derived it yet, so I am going to discuss some partial results in this direction (under certain assumptions I proved that the answer is a linear combination of 3 expressions which are known explicitly)
Seminar's sites:

http://crei.skoltech.ru/cas/ru/calendar-ru/sem-wed-ru/

https://crei.skoltech.ru/cas/calendar/sem-wed/