Moderately non-loca η(η)over-bar vertices in the AdS4 higher-spin gauge theory

A new concept of moderate non-locality in higher-spin gauge theory is introduced. Based on the recently proposed differential homotopy approach, amoderately nonlocal scheme, that is softer than those resulting from the shifted homotopy approach available in the literature so far, is worked out in the mixed eta(eta) over bar sector of the Vasiliev higher-spin theory. To calculate moderately non-local vertices gamma(eta(eta) over bar) (omega, C, C, C) for all ordering of the fields psi and C we apply an interpolating homotopy, that respects the moderate non-locality in the perturbative analysis of the higher-spin equations.