We study integrated correlation functions of half-BPS operators in SU(N) \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory (SYM) involving two superconformal primary operators in the stress-tensor multiplet and two identical maximal-trace operators of arbitrary R-charge p. Thanks to \( \mathcal{N}=4 \) SYM electro-magnetic duality these integrated correlators have recently been computed as exact functions of N, p, and of the Yang-Mills complexified coupling τ. Using a combination of tools from SL(2, ℤ) spectral theory and resurgence analysis, we study the landscape of large-N and/or large-charge expansions for these correlators. In particular, we find novel non-perturbative effects in the limit where N → ∞ with p/N2 fixed. From a holographic point of view this double-scaling regime is deeply connected with a second family of correlators which we analyse. Using the results for the maximal-trace operators, we derive an exact expression for a new integrated correlator involving two coherent-state operators, defined via an exponential generating function of multi-graviton states. At large-N this correlator admits a holographic dual description in terms of a back-reacted geometry known as the AdS bubble. First, we show that the leading supergravity contribution to the integrated correlator agrees with a direct explicit integration of the correlator itself. Secondly, we derive predictions for the integrated version of the Virasoro-Shapiro amplitude evaluated on the AdS bubble background. Lastly, we demonstrate that the large-N non-perturbative contributions to this integrated correlator emerge from giant-magnon configurations in the dual AdS bubble
