Towards Bootstrapping F-theory

TL;DR

This paper explores F-theory realizations via type IIB string theory with D3 and sevenbranes, using matrix models and bootstrap techniques to analyze large N limits, flavor symmetries, and holographic correlators, connecting field theory and string theory insights.

Contribution

It introduces novel matrix models with non-polynomial potentials to compute free energies and uses bootstrap methods to determine correlators in F-theory related CFTs.

Findings

Computed the large N free energy F(m) using matrix models.

Fixed the logarithmic threshold in holographic correlators.

Matched flat space predictions with holographic results.

Abstract

We consider type IIB string theory with $N$ D3 branes and various configurations of sevenbranes, such that the string coupling $g_s$ is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual to rank $N$ Argyres-Douglas conformal field theories (CFTs) with $SU(2)$ and $SU(3)$ flavor groups, and Minahan-Nemeschansky CFTs with $E_6, E_7$ and $E_8$ flavor groups. We use the Seiberg-Witten curves of these theories to compute the mass deformed sphere free energy $F(m)$ at large $N$ in terms of novel matrix models with non-polynomial potentials. We show how $F(m)$ can be used along with the analytic bootstrap to fix the large $N$ expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on $AdS_5\times S^3$, and in the flat space limit determine the effective theory of sevenbranes in F-theory. As a first step in this program, we use the matrix models to compute the $\log N$ term in $F(m)$ and thereby fix the logarithmic threshold in the $AdS_5\times S^3$ holographic correlator, which matches the flat space prediction.