Moderately non-local $\eta \bar\eta$ vertices in the $AdS_4$ higher-spin gauge theory

TL;DR

This paper introduces a new moderate non-locality concept in higher-spin gauge theory, utilizing a differential homotopy approach to compute non-local vertices more smoothly than previous methods.

Contribution

It develops a moderately non-local scheme in higher-spin theory using an interpolating homotopy, improving upon existing shifted homotopy techniques.

Findings

Successfully computes $mbda^{taarta}$ vertices for all field orderings.

Demonstrates the scheme's smoother non-locality properties.

Provides a new computational approach for higher-spin interactions.

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 issofter than those resulting from the shifted homotopy approach available in the literature so far, is worked out in the mixed $\eta\bar\eta$ sector of the Vasiliev higher-spin theory. To calculate moderately non-local vertices $\Upsilon^{\eta\bar \eta}(\omega, C,C,C)$ for all ordering of the fields $\omega$ and $C$ we apply an interpolating homotopy, that respects the moderate non-locality in the perturbative analysis of the higher-spin equations.