Multiple mirror manifolds and topology change in string theory

Abstract

We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the 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 numerous topologically distinct Calabi-Yau manifolds for its geometric interpretation. A single family of continuously connected conformal theories thereby probes a host of topologically distinct geometrical spaces giving rise to multiple mirror manifolds.

Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

“…For example, from F (A) we obtain, up to degree eight, instanton contributions n r i,0,0,0,0 with alternating sign , respectively, are those that are shrunk to zero volume and whose corresponding invariant changes sign under the process of the four possible flop operations interrelating them, starting from resolution A (cf. the discussion in [32]). For certain directions in the Kähler cone e.g.…”

Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces

“…We can now describe the monomial-divisor mirror map [33] for these models. Some evidence for the existence of such a map was given by the computations in [34].…”

Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds

“…Then Sp(2) ⊂ Sp(2) × Sp(1) acts on this four-sphere via the usual action of Spin(5) ∼ = Sp (2). Consider the subgroup U(2) ⊂ Sp(2).…”