On the Regularization of Extremal Three-point Functions Involving Giant Gravitons

TL;DR

This paper revisits the regularization method used in calculating extremal three-point functions involving giant gravitons in AdS_5/CFT_4, proposing a reformulation that extends to the ABJM setup where such functions are not protected.

Contribution

It reformulates the regularization procedure for extremal three-point functions, enabling its application to non-protected operators in the ABJM theory.

Findings

Regularization procedure is clarified and generalized.

Match between gauge and string theory is confirmed in AdS_5/CFT_4.

Extension to ABJM theory where protection does not hold.

Abstract

In the AdS_5/CFT_4 set-up, extremal three-point functions involving two giant 1/2 BPS gravitons and one point-like 1/2 BPS graviton, when calculated using semi-classical string theory methods, match the corresponding three-point functions obtained in the tree-level gauge theory. The string theory computation relies on a certain regularization procedure whose justification is based on the match between gauge and string theory. We revisit the regularization procedure and reformulate it in a way which allows a generalization to the ABJM set-up where three-point functions of 1/2 BPS operators are not protected and where a match between tree-level gauge theory and semi-classical string theory is hence not expected.