Dynamics of Heavy Operators in $\mathcal{N}=4$ SYM: Integrated Correlators and AdS Bubbles
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2026
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| _version_ | 1866917248741933056 |
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| author | Aprile, Francesco Dorigoni, Daniele Treilis, Rudolfs |
| author_facet | Aprile, Francesco Dorigoni, Daniele Treilis, Rudolfs |
| contents | 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 ${\rm SL}(2,\mathbb{Z})$ 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 $N\rightarrow \infty$ with $p/N^2$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_04963 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamics of Heavy Operators in $\mathcal{N}=4$ SYM: Integrated Correlators and AdS Bubbles Aprile, Francesco Dorigoni, Daniele Treilis, Rudolfs High Energy Physics - Theory 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 ${\rm SL}(2,\mathbb{Z})$ 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 $N\rightarrow \infty$ with $p/N^2$ 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. |
| title | Dynamics of Heavy Operators in $\mathcal{N}=4$ SYM: Integrated Correlators and AdS Bubbles |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.04963 |