Wednesday 17 July 2013

Conifold as Word

Continuation of Quantum Theory for Language

Conifold as Word

   TANAKA Akio

1 Conifold is presented by the following.
n-dimensional complex projective space that has homogeneous coordinates (z1, z2, … , zn+1) is given the following condition.
|z1|2 +| z22+ … + | zn+1|2 = r    r>0
There emerges 2n+1-dimensional sphere S2n+1.
On arbitrary θ, when identification is done with the polar coordinate representation, Pn is presented.
(z1, z2, …, zn+1) ~ (ez1, ez2, … ezn+1)
P1 that has line bundle’s direct sum O(-1)   O(-1) is conifold.
P1 has homogeneous coordinates  (z1z2) and line bundle coordinates (z3, z4).
Conifold that is also called local Pis defined by the following.
|z1|2 +| z22- | z3|2 - | z4|2 = r 
When | z3|2 = | z4|2 = 0,  |z1|2 +| z22 = r  is given as 2-dimensional sphere S2 that is called resolved conifold.
When complexification of parameter r becomes 0, there emerges conifold with singularity.
From here, deformed conifold is given by the blowing up resolved conifold.
Deformed conifold has 3-dimensional sphere S3 that wraps D6 brane.
Here  S3 is identificated to word. Brane is identificated to grammar.
Further now topology R4 ×S3 is presented.
This topology is identificated to sentence.      


Tokyo June 9, 2007

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