Giant Graviton Integrated Correlators at Finite Coupling and All Orders in 1/N

We study the giant graviton integrated correlator in SU(N) N=4 super-Yang-Mills at finite complexified coupling τ. Despite the formidable complexity arising from the heavy nature of the operators considered, the large-N expansion simplifies dramatically and exhibits manifest modular invariance. At each order in 1/N, the expansion coefficients are linear combinations of nonholomorphic Eisenstein series, thus capturing the full spectrum of perturbative and nonperturbative effects in the Yang-Mills coupling. Furthermore, we find additional contributions, which are modular functions exponentially suppressed in N. In the 't Hooft limit, this yields an all-orders result in the 1/N expansion at arbitrary coupling λ, extending beyond prior results of leading orders. For the U(N) theory, we obtain a closed-form expression valid for all N and τ and show that the coupling-dependent sector of the large-N expansion is universal between SU(N) and U(N) to all orders. Crucially, we exploit the integrated correlator constraints and determine the giant graviton correlator itself to two-loop order at finite N, previously only accessible in the planar limit.