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

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 image considered in [C. Gomez, S. Montanez, A comment on quantum distribution functions and the OSV conjecture, ] to test OSV conjecture. We first study toric realizations of image and then build a toric representation of image using intersections of local Calabi–Yau threefolds image. We develop the 2d image 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 image with image a k-dim integer vector and image a compact complex one dimension base consisting of the intersection of k 2-spheres image with generic intersection matrix image. 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 image. A comment on the link between our analysis and the construction of [N. Caporaso, M. Cirafici, L. Griguolo, S. Pasquetti, D. Seminara, R.J. Szabo, Topological strings, two-dimensional Yang–Mills theory and Chern–Simons theory on torus bundles, ] is also given.