Open problems

We did not verify that of Eq. (66) satisfies the conditions formulated in Mikhailov:2016myt,Mikhailov:2016rkp. In particular, we may hope for , but more complicated scenarios are also possible. We believe that the invariance of our construction under the symmetries of is important to satisfy those conditions at the quantum level.

We did not explicitly calculate the restriction of the to the standard family of Lagrangian submanifolds, corresponding to the integration over the space of metrics. It can probably be expressed in terms of where as calculated in Berkovits:2010zz. In any case, it is most likely nonzero, and therefore the string measure of Eq. (1) is not just the product of Beltrami differentials, but involves also the curvature terms .