Global topology of the Hitchin system - GEOM
Global topology of the Hitchin system - GEOM
Global topology of the Hitchin system - GEOM
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Strominger-Yau-Zaslow<br />
X CY 3-fold<br />
Y mirror CY 3-fold<br />
B is 3-dimensional real manifold - mostly S 3<br />
X 6<br />
<br />
Y<br />
<br />
<br />
π <br />
<br />
6<br />
<br />
ˆπ <br />
B3 π and ˆπ are special Lagrangian fibrations<br />
for generic x ∈ B 3<br />
Lx = π −1 (x) ∼ = T 3 and ˆLx = ˆπ −1 (x) ∼ = T 3 are dual special<br />
Lagrangian tori<br />
generically Y 6 can be thought <strong>of</strong> as <strong>the</strong> moduli space <strong>of</strong> flat<br />
U(1) connections on a generic fiber Lx (a.k.a. D-branes)<br />
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