Spin-locality of η 2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ quartic higher-spin vertices

Abstract

Abstract Higher-spin theory contains a complex coupling parameter η. Different higher-spin vertices are associated with different powers of η and its complex conjugate η ¯ $$ \overline{\eta} $$ . Using Z-dominance Lemma of [1], that controls spin-locality of the higher-spin equations, we show that the third-order contribution to the zero-form B(Z; Y; K) admits a Z-dominated form that leads to spin-local vertices in the η 2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ sectors of the higher-spin equations. These vertices include, in particular, the η 2 and η ¯ 2 $$ {\overline{\eta}}^2 $$ parts of the ϕ 4 scalar field vertex.

Keywords

• Higher Spin Gravity
• Higher Spin Symmetry