CMSA Mathematical Physics Seminar: Moduli Space Holography and the Finiteness of Flux Vacua

In this talk I describe a holographic perspective to study field spaces that arise in string compactifications. The constructions are motivated by a  general description of the asymptotic, near-boundary regions in complex structure moduli spaces of Calabi-Yau manifolds using asymptotic Hodge theory. For real two-dimensional field spaces, I introduce an auxiliary bulk theory and describe aspects of an associated sl(2) boundary theory. The bulk reconstruction from the boundary data is provided by the sl(2)-orbit theorem of Schmid and Cattani, Kaplan, Schmid, which is a famous and general result in Hodge theory. I then apply this correspondence to the flux landscape of Calabi-Yau fourfold compactifications and discuss how this allows us, in work with C. Schnell, to prove that the number of self-dual flux vacua is finite.

Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09