Generalization to correlators with several heavy insertions

Establish whether the worldline effective-field-theory formalism for heavy-heavy-light-light correlators generalizes to correlators with several heavy insertions, and determine whether response data extracted from heavy-heavy-light-light correlators satisfy consistency relations with the local counterterms required in heavy-heavy-heavy-heavy and more general heavy-light correlators.

Background

The paper develops a worldline effective description for a single heavy state probed by light operators and establishes a map between worldline response coefficients and heavy-light CFT data. The discussion identifies an unresolved extension to correlators containing several heavy insertions. The proposed problem is to test whether the response coefficients are intrinsic properties of the heavy state rather than probe-dependent quantities, by relating data extracted from HHLL correlators to counterterms needed in HHHH and other multi-heavy correlators. Such an extension would also involve nonlinear worldline operators describing higher-order tidal response and radiation.