$$ \mathcal{N}=2 $$ universality at strong coupling

A bstract We present a detailed analysis of integrated correlators for an $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> 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 $$ \mathcal{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math> with respect to the fundamental mass ( μ ), the anti-symmetric mass ( m ) and the squashing parameter ( b ), corresponding to integrated insertions of the $$ \mathcal{N}=2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> 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 $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> SYM. Our main result is a remarkable universality for the mixed gluon-graviton scattering amplitudes off D7-branes, obtained from $$ {\partial}_{\mu}^2{\partial}_m^2\log \mathcal{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>log</mml:mo> <mml:mi>Z</mml:mi> </mml:math> and $$ {\partial}_{\mu}^2{\partial}_b^2\log \mathcal{Z} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:msubsup> <mml:mi>∂</mml:mi> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>log</mml:mo> <mml:mi>Z</mml:mi> </mml:math> . 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 $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> 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 AdS 5 brane-string amplitudes and highlights an unexpected universality across distinct superconformal theories at strong coupling.