4 research outputs found
Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
Motivated by studies on 4d black holes and q-deformed 2d Yang Mills theory,
and borrowing ideas from compact geometry of the blowing up of affine ADE
singularities, we build a class of local Calabi-Yau threefolds (CY^{3})
extending the local 2-torus model \mathcal{O}(m)\oplus \mathcal{O}(-m)\to
T^{2\text{}} considered in hep-th/0406058 to test OSV conjecture. We first
study toric realizations of T^{2} and then build a toric representation of
X_{3} using intersections of local Calabi-Yau threefolds \mathcal{O}(m)\oplus
\mathcal{O}(-m-2)\to \mathbb{P}^{1}. We develop the 2d \mathcal{N}=2 linear
\sigma-model for this class of toric CY^{3}s. Then we use these local
backgrounds to study partition function of 4d black holes in type IIA string
theory and the underlying q-deformed 2d quiver gauge theories. We also make
comments on 4d black holes obtained from D-branes wrapping cycles in
\mathcal{O}(\mathbf{m}) \oplus \mathcal{O}(\mathbf{-m-2}%) \to \mathcal{B}_{k}
with \mathbf{m=}(m_{1},...,m_{k}) a k-dim integer vector and \mathcal{B}_{k} a
compact complex one dimension base consisting of the intersection of k
2-spheres S_{i}^{2} with generic intersection matrix I_{ij}. We give as well
the explicit expression of the q-deformed path integral measure of the
partition function of the 2d quiver gauge theory in terms of I_{ij}.Comment: 36 pages, latex, 9 figures. References adde