Moduli Space Holography and the Finiteness of Flux Vacua

Understand

A holographic perspective to study and characterize field spaces that arise in string compactifications is suggested.

• A concrete correspondence is developed by studying two-dimensional moduli spaces in supersymmetric string compactifications.
• It is proposed that there exist theories on the boundaries of each moduli space, whose crucial data are given by a Hilbert space, an Sl(2,C)-algebra, and two special operators.
• This boundary data is motivated by asymptotic Hodge theory and the fact that the physical metric on the moduli space of Calabi-Yau manifolds asymptotes near any infinite distance boundary to a Poincare metric with Sl(2,R) isometry.