Towards Bootstrapping F-theory

TL;DR

The paper develops a nonperturbative framework to probe stringy corrections in simple F-theory setups by leveraging Seiberg–Witten curves to map mass-deformed theories to matrix models with non-polynomial potentials. From the large-$N$ expansion of the resulting matrix model, the authors extract the leading $ ext{log}N$ term in the sphere free energy $F(m)$ and use an integrated correlator constraint to fix the logarithmic threshold $b_{ ext{log}}$ in the holographic Mellin amplitude for gluon scattering on $AdS_5 imes S^3$, with the flat-space limit matching the sevenbrane effective theory. The key result is a universal relation $b_{ ext{log}}=rac{6}{ abla}$ (where $ abla=rac{h^ v +6}{6}$ is the scaling parameter tied to the Coulomb-branch data) that reproduces known $D_4$ values ($b_{ ext{log}}=3$) and provides new predictions for other ADE/MN theories. This work demonstrates a concrete path to compute stringy corrections in F-theory CFTs by combining SW techniques, non-polynomial matrix models, and bootstrap constraints, and it lays groundwork for higher-derivative ($F^4$) terms and finite-$N$ analyses with potential phenomenological implications for brane dynamics in F-theory compactifications.

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.