Gravity-gauge anomaly constraints on the energy-momentum tensor

Abstract

We derive constraints on the four dimensional energy-momentum tensor from gravitational and gauge anomalies. Our work can be considered an extension of Duff’s analysis [1] to include parity-odd terms and explicit symmetry breaking. The constraints imply the absence of the parity-odd RR~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ R\\overset{\\sim }{R} $$\\end{document} and FF~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ F\\overset{\\sim }{F} $$\\end{document} terms, for theories whose symmetries are compatible with dimensional regularisation, in a model-independent way. Remarkably, even in the case of explicit symmetry breaking the □R-anomaly is found to be finite and unambiguous after applying the symmetry constraints. We compute mixed gravity-gauge anomalies at leading order and deduce phenomenological consequences for vector bosons associated with global chiral symmetries.