Black holes in type IIA string on Calabi–Yau threefolds with affine ADE geometries and q-deformed 2d quiver gauge theories

This is the authors' abstract. We don't add key points for this paper.

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 (CY³) extending the local 2-torus model (m)\⊕ (-m)\→ T2\ considered in hep-th/0406058 to test OSV conjecture. We first study toric realizations of T² and then build a toric representation of X₃ using intersections of local Calabi-Yau threefolds (m)\⊕ (-m-2)\→ ¹. We develop the 2d =2 linear \σ-model for this class of toric CY³s. 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 () \⊕ (\-m-2%) \→ ₖ with =(m₁,...,mₖ) a k-dim integer vector and ₖ a compact complex one dimension base consisting of the intersection of k 2-spheres Sᵢ² with generic intersection matrix Iᵢⱼ. 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 Iᵢⱼ.