Semiclassics, branes, and extremality

We revisit the problem of computing extremal and non-extremal three point functions of semiclassical probes with single trace operators and point out certain inconsistencies in previous approaches in the literature. We clarify the roles of wavefunctions and averaging over moduli, concluding that holographic computations may be performed with or without averaging. By carefully implementing the extrapolate dictionary for extremal correlators we explain the origin of the apparent mismatch between supergravity and CFT for extremal correlators involving giant gravitons in type IIB supergravity. We propose an ansatz for the wavefunctions of half-BPS giants which reproduces large $N$ limit of certain extremal two and three point functions in $\mathcal{N}=4$ SYM.

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