Exact large charge in N=4 SYM and semiclassical string theory

In four-dimensional 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 tau. This permits a systematic and non-perturbative large charge expansion for any N and tau. Especially novel is a double-scaled gravity regime in which p similar to N-2 >> 1, holographically dual to a large charge regime of semiclassical type IIB string theory in AdS(5) x S-5. 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.

Automated summary

In this paper, we study a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge in four-dimensional N = 4 super Yang-Mills theory with gauge group SU(N). We show that these integrated correlators are 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 is exact in the R-charge p, rank N, and complexified gauge coupling tau, allowing for a systematic and non-perturbative large charge expansion.