Abstract
In the AdS5/CFT4 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.
Highlights
In the AdS5/CFT4 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
After the successful application of integrability techniques to the planar spectral problem of the AdS5/CFT4 set-up [1], the calculation of three-point functions in the same set-up has attracted renewed attention with some recent highlights being the conjecture of an all loop formula for three-point functions of single trace operators in certain sub-sectors of N = 4 SYM [2] and the formulation of certain integrability axioms for the cubic string theory vertex [3]
Our three-point functions involve giant gravitons which in the string theory language correspond to higher dimensional Dor M-branes wrapping certain submanifolds of the string theory background and which in the gauge theory picture are represented by specific linear combinations of multi-trace operators, namely Schur polynomials
Summary
In the AdS5/CFT4 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. On the regularization of extremal three-point functions involving giant gravitons
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