Symplectic Language Theory
Note3
Mirror Symmetry Conjecture on Rational Curve
[Conjecture]
Mirror relation
M, Mmir
M is manifold.
Mmir is 3-dimensional Calabi-Yau manifold.
Definition of Calabi-Yau manifold, the next is determined.
Yukawa combination
Mirror map Mir :
The upper's left is seemed as moduli space's tangent space at M's symplectic structure.
The next conjecture is satisfied.
The upper's right side is below.
F is Gromov-Witten potential.
[Conjecture]
Mirror relation
M, Mmir
M is manifold.
Mmir is 3-dimensional Calabi-Yau manifold.
Definition of Calabi-Yau manifold, the next is determined.
Yukawa combination
Mirror map Mir :
The upper's left is seemed as moduli space's tangent space at M's symplectic structure.
The next conjecture is satisfied.
The upper's right side is below.
F is Gromov-Witten potential.
[Note]
1
Actual language is given by manifold M.
2
Mirror language is given by Calabi-Yau manifold Mmir.
3
Deformation of Mmir is expressed by
.
4
Relation between actual language and mirror language is given by the mirror map and the conjecture.
[References]
<Early papers on the theme>
<Present consideration>
To be continued
Tokyo February 27, 2009
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