ausblenden:
Schlagwörter:
High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Algebraic Geometry, math.AG,Mathematics, Mathematical Physics, math.MP
Zusammenfassung:
The number of BPS bound states of D-branes on a Calabi-Yau manifold depends
on two sets of data, the BPS charges and the stability conditions. For D0 and
D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold $X$, both are
naturally related to the K\"ahler moduli space ${\cal M}(X)$. We construct
unitary one-matrix models which count such BPS states for a class of toric
Calabi-Yau manifolds at infinite 't Hooft coupling. The matrix model for the
BPS counting on $X$ turns out to give the topological string partition function
for another Calabi-Yau manifold $Y$, whose K\"ahler moduli space ${\cal M}(Y)$
contains two copies of ${\cal M}(X)$, one related to the BPS charges and
another to the stability conditions. The two sets of data are unified in ${\cal
M}(Y)$. The matrix models have a number of other interesting features. They
compute spectral curves and mirror maps relevant to the remodeling conjecture.
For finite 't Hooft coupling they give rise to yet more general geometry
$\widetilde{Y}$ containing $Y$.
