N=2 universality at strong coupling

We present a detailed analysis of integrated correlators for an N=2 supercon-formal field theory on a squashed sphere with SU(N) gauge group and fundamental/anti-symmetric matter. Employing the matrix model arising from supersymmetric localisation, we compute derivatives of the partition function Z with respect to the fundamental mass (μ), the anti-symmetric mass (m) and the squashing parameter (b), corresponding to integrated insertions of the N=2 flavour-current and stress-tensor multiplets, which are holographically dual to gluon and graviton scatterings in the presence of D7-branes. For correlators dual to only graviton scatterings, we confirm the planar-limit equivalence with N=4 SYM. Our main result is a remarkable universality for the mixed gluon-graviton scattering amplitudes off D7-branes, obtained from ∂μ2∂m2logZ and ∂μ2∂b2logZ. We show that the leading and sub-leading large-N contributions in the strong-coupling regime are governed by universal asymptotic series, identical to those found for integrated giant-graviton correlators in N=4 SYM. We also propose an SL(2, ℤ)-invariant completion of these results in terms of non-holomorphic Eisenstein series. This completion provides exact constraints on higher-derivative terms in the dual AdS₅ brane-string amplitudes and highlights an unexpected universality across distinct superconformal theories at strong coupling.