Abstract
In four-dimensional \( \mathcal{N} \) = 4 super Yang-Mills theory with gauge group SU(N), we present a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge. These integrated correlators are shown to be equivalent to a one-dimensional semi-infinite lattice of harmonic oscillators with nearest-neighbor interactions, evolving over the fundamental domain of SL(2, ℤ). The solution, exceptionally simple in an SL(2, ℤ)-invariant eigenbasis, is exact in the R-charge p, rank N, and complexified gauge coupling τ. This permits a systematic and non-perturbative large charge expansion for any N and τ. Especially novel is a double-scaled “gravity regime” in which p ~ N2 ≫ 1, holographically dual to a large charge regime of semiclassical type IIB string theory in AdS5 × S5. Our results in this limit provide a holographic computation of integrated semiclassical string amplitudes at arbitrary string coupling, including an emergent string scale with a large charge dressing factor. We compare to extremal correlators in superconformal QCD, for which we predict new genus expansions at large charge scaling with N.
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Acknowledgments
We thank Scott Collier, Abhijit Gadde, Francesco Galvagno, Simeon Hellerman, Dileep Jatkar, Shota Komatsu, Grisha Korchemsky, Gautam Mandal, Mark Mezei and Ioannis Tsiares for discussions. This research was supported by ERC Starting Grant 853507, and in part by the National Science Foundation under Grant No. NSF PHY-1748958.
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Paul, H., Perlmutter, E. & Raj, H. Exact large charge in \( \mathcal{N} \) = 4 SYM and semiclassical string theory. J. High Energ. Phys. 2023, 78 (2023). https://doi.org/10.1007/JHEP08(2023)078
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DOI: https://doi.org/10.1007/JHEP08(2023)078