| Summary: | Abstract A new concept of moderate non-locality in higher-spin gauge theory is introduced. Based on the recently proposed differential homotopy approach, a moderately non-local scheme, that is softer than those resulting from the shifted homotopy approach available in the literature so far, is worked out in the mixed $$\eta {\bar{\eta }}$$ η η ¯ sector of the Vasiliev higher-spin theory. To calculate moderately non-local vertices $$\Upsilon ^{\eta \bar{\eta }}(\omega , C,C,C)$$ Υ η η ¯ ( ω , C , C , C ) for all ordering of the fields $$\omega $$ ω and C we apply an interpolating homotopy, that respects the moderate non-locality in the perturbative analysis of the higher-spin equations.
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