On the Local Frame in Nonlinear Higher-Spin Equations

TL;DR

This paper investigates the properties of the local resolution operator in higher-spin equations, revealing how it ensures local interactions and differs from the conventional resolution by a non-local shift.

Contribution

It formulates conditions on master fields that enforce locality and derives the Green function for zero-forms with opposite helicities in higher-spin theory.

Findings

The local resolution operator differs from the standard De Rham resolution by a non-local shift.

Conditions on master fields restrict dependence on spinor variables and index contractions.

Green function for zero-forms with opposite helicities is explicitly constructed.

Abstract

Properties of the resolution operator ${\rm d}_{loc}^*$ in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor $Y$, $Z$ variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution ${\rm d}_{loc}^*$ differs from the conventional De Rham resolution ${\rm d}_Z^*$ by a non-local shift.