Spin-locality of η 2 and η ˉ 2 documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {overline{eta}}^2 $$end{document} quartic higher-spin vertices

摘要

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 η ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ overline{eta} $$end{document} . 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 ˉ 2 documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {overline{eta}}^2 $$end{document} sectors of the higher-spin equations. These vertices include, in particular, the η ~(2)and η ˉ 2 documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ {overline{eta}}^2 $$end{document} parts of the ? ~(4)scalar field vertex.