Mirror Symmetry and the Type II String

TL;DR

This paper explores how mirror symmetry between Calabi-Yau threefolds extends to an isomorphism of type II string theories, revealing unexpected dependencies in the moduli space structure and nonperturbative effects.

Contribution

It investigates the implications of mirror symmetry for the structure of semiclassical moduli spaces in type II string theories, highlighting novel dependencies in the Ramond-Ramond scalars.

Findings

Discrete shifts in Ramond-Ramond scalars depend on the B-field unexpectedly.

Mirror symmetry extends to an isomorphism of type IIA and IIB string theories with nonperturbative effects.

Insights into the structure of moduli spaces in compactified type II theories.

Abstract

If $X$ and $Y$ are a mirror pair of Calabi--Yau threefolds, mirror symmetry should extend to an isomorphism between the type IIA string theory compactified on $X$ and the type IIB string theory compactified on $Y$, with all nonperturbative effects included. We study the implications which this proposal has for the structure of the semiclassical moduli spaces of the compactified type II theories. For the type IIB theory, the form taken by discrete shifts in the Ramond-Ramond scalars exhibits an unexpected dependence on the $B$-field. (Based on a talk at the Trieste Workshop on S-Duality and Mirror Symmetry.)