The Large N Limit of ${\cal N} =2,1 $ Field Theories from Threebranes in F-theory

TL;DR

This paper investigates the large N behavior of ${ m N}=2,1$ supersymmetric field theories derived from D3-branes in F-theory, analyzing their spectra, symmetries, and deformations through string dualities and supergravity solutions.

Contribution

It provides a detailed computation of the chiral primary spectrum and global symmetries for these theories, including fractional dimensions at Argyres-Douglas points, and compares results with field theory for the $D_4$ singularity.

Findings

Agreement between supergravity and field theory results for large N in the $D_4$ case.

Identification of operators with fractional conformal dimensions at Argyres-Douglas points.

Construction of supergravity solutions for deformations away from conformal points.

Abstract

We consider field theories arising from a large number of D3-branes near singularities in F-theory. We study the theories at various conformal points, and compute, using their conjectured string theory duals, their large $N$ spectrum of chiral primary operators. This includes, as expected, operators of fractional conformal dimensions for the theory at Argyres-Douglas points. Additional operators, which are charged under the (sometimes exceptional) global symmetries of these theories, come from the 7-branes. In the case of a $D_4$ singularity we compare our results with field theory and find agreement for large $N$. Finally, we consider deformations away from the conformal points, which involve finding new supergravity solutions for the geometry produced by the 3-branes in the 7-brane background. We also discuss 3-branes in a general background.