Towards Bootstrapping F-theory

We consider type IIB string theory with N D3 branes and various configurations of sevenbranes, such that the string coupling gₛ 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 E₆, E₇ and E₈ 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 AdS₅× S³, 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 AdS₅× S³ holographic correlator, which matches the flat space prediction.