A Note on the Stringy Embeddings of Certain N = 2 Dualities

TL;DR

This paper explores how certain N=2 dualities, including Seiberg-Witten and Gaiotto models, can be embedded in F-theory, providing insights into their dualities, non-conformal extensions, and the associated geometric and quantum corrections.

Contribution

It demonstrates the embedding of Gaiotto models in F-theory, extending the understanding of N=2 dualities and their non-conformal and cascading behaviors.

Findings

F-theory embeddings clarify duality structures.

Near horizon geometries capture UV and IR behaviors.

Non-perturbative corrections relate to gauge theory instantons.

Abstract

Seiberg-Witten theory can be embedded in F-theory using D3 branes probing an orientifold geometry. The non-perturbative corrections in the orientifold picture map directly to the instanton corrections in the corresponding gauge theory that convert the classical moduli space to the quantum one. In this short review we argue that the recently proposed class of conformal Gaiotto models may also be embedded in F-theory. The F-theory constructions help us not only to understand the Gaiotto dualities but also to extend to the non-conformal cases with and without cascading behaviors. For the conformal cases, the near horizon geometries in F-theory capture both the UV and IR behaviors succinctly.