Holographic two-point functions of heavy operators revisited

A bstract In this paper we investigate the holographic computation of the two-point functions of $$\\frac{1}{2}$$ -BPS chiral primary operators with scaling dimensions ∆ ~ N or ∆ ~ N 2 in 𝒩 = 4 SU ( N ) SYM using Type IIB supergravity. First we consider giant graviton operators, resolving ambiguities in the previous literature on holographic computation of the two-point function, and make a new proposal for this calculation. We argue that the D3-brane action for the giant gravitons (as well as for their $$\\frac{1}{4}$$ - and $$\\frac{1}{8}$$ -BPS counterparts) should contain additional boundary terms which arise naturally from the path integral and which are required to make the variational problem well-defined. We derive the form of these terms and show that the corrected action has an on-shell value that reproduces the two-point function of the gauge theory operators. Moreover, we demonstrate that these boundary terms are necessary building blocks for the giant graviton three-point functions, and we reproduce the coordinate dependence of the extremal three-point function as a saddle-point for the boundary action. Then we consider operators with ∆ ~ N 2 and calculate the two-point function by evaluating the Gibbons-Hawking-York boundary term in the Type IIB pseudo-action in the Lin-Lunin-Maldacena bubbling geometry background.