“Bootstrapping F-theory”

We consider a set of 4d N=2 SCFTs defined by N D3 branes probing F-theory singularities with constant value of the axio-dilaton. In these theories we focus on the four-point function of the moment map operator at large N, which is holographically dual to a gluon amplitude in AdS_5 x S^3. We use the relation between a certain integral of the correlator to the mass-deformed sphere free energy of the theory to put constraints on this observable at the first few orders in the 1/N expansion. In the only case admitting a gauge theory description, we can use standard techniques of supersymmetric localization and fix the coefficients of certain higher-derivative terms in the F-theory effective action as functions of the axio-dilaton. On the other hand, the other theories do not have a Lagrangian but we are still able to use their Seiberg-Witten description to fix a logarithmic threshold term in the gluon amplitude, which is regulated by string theory. Our result agrees with the prediction from the flat space limit. This is the first step towards fixing the coefficients of higher-derivative terms in the F-theory effective action using supersymmetric localization, even for strongly coupled fixed points.