F-theory, Seiberg-Witten curves and $ \mathcal{N} = {2} $ dualities

Abstract

F-theoretic constructions can alternatively be understood as consequences of certain N = 2 Seiberg-Witten theories via type IIB r D3s probing the quantum corrected orientifold backgrounds. We present four models that come out from such consideration. In Model 1, the 7-branes wrap the flat R^4 directions, leading to the well known Sp(2r) theories. We study singularity structure of moduli space of Seiberg-Witten curve, such as maximal Argyres-Douglas loci, in order to construct 1-1 map between moduli spaces. In Model 2, the 7-branes are wrapped on Taub-NUT and multi Taub-NUT spaces instead of R^4. These configurations may explain many of the Gaiotto-type constructions including possible extensions to non-conformal models with cascading behaviors. In this model the UV is described by the probe D3s decomposed into D5-anti D5 pairs wrapped on multi Taub-NUT space, while the IR remains a 4d theory. For certain arrangements of the 7-branes, this model may be dualized to the brane networks of Benini, Benvenuti and Tachikawa. The Gaiotto dualities in Model 2 are explained by chiral anomaly cancellations, anti-GSO projections and brane transmutations. Model 3 is described by seven-branes wrapped on a K3 manifold and D3 and anti-D3 probes whose number may differ at most by 24. These constructions could lead to new N = 2 models with possible dualities to both type IIB and heterotic theories on non-Kahler manifolds. In the limit where the number of probes becomes very large, the physics is captured by M(atrix) theory on K3 x K3 manifold. Finally, Model 4 is described by k D3s probing intersecting seven-brane backgrounds with Sp(2k) x Sp(2k) gauge group. These constructions could produce new N =1 heterotic dual on a non-Kahler K3 manifold that is no longer conformally Calabi-Yau. We discuss possible constraints on these models coming from global charge and anomaly cancellations in F-theory.