Multiple Mirror Manifolds and Topology Change in String Theory

TL;DR

This paper demonstrates how mirror symmetry in string theory allows for smooth topology change between different Calabi-Yau manifolds, revealing a rich moduli space with multiple mirror pairs.

Contribution

It provides the first concrete example of topology change in string theory using mirror symmetry, connecting quantum theories on topologically distinct spaces.

Findings

Quantum theories on different target spaces can be smoothly connected.

The moduli space includes numerous topologically distinct Calabi-Yau manifolds.

Multiple mirror manifolds are connected within a single conformal field theory family.

Abstract

We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the {\it quantum theories} based on certain nonlinear sigma models with topologically distinct target spaces can be smoothly connected even though classically a physical singularity would be encountered. We accomplish this by rephrasing the description of these nonlinear sigma models in terms of their mirror manifold partners--a description in which the full quantum theory can be described exactly using lowest order geometrical methods. We establish that, for the known class of mirror manifolds, the moduli space of the corresponding conformal field theory requires not just two but {\it numerous} topologically distinct Calabi-Yau manifolds for its geometric interpretation. A {\it single} family of continuously connected conformal theories thereby probes a host of topologically distinct geometrical spaces giving rise to {\it multiple mirror manifolds}.