Spin-locality of η2 and $$ {\overline{\eta}}^2 $$ quartic higher-spin vertices
V. E. Didenko, O. A. Gelfond, A. V. Korybut, M. A. Vasiliev
Abstract
A bstract Higher-spin theory contains a complex coupling parameter η . Different higher-spin vertices are associated with different powers of η and its complex conjugate $$ \overline{\eta} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>η</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . 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 $$ {\overline{\eta}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mover> <mml:mi>η</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msup> </mml:math> sectors of the higher-spin equations. These vertices include, in particular, the η 2 and $$ {\overline{\eta}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mover> <mml:mi>η</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msup> </mml:math> parts of the ϕ 4 scalar field vertex.