Abelian Vectors and Self-Dual Tensors in Six-Dimensional Supergravity

Abstract

In this note we describe the most general coupling of {\it abelian} vector and tensor multiplets to six-dimensional $(1,0)$ supergravity. As was recently pointed out, it is of interest to consider more general Chern-Simons couplings to abelian vectors of the type $H^r=d{B}^r-1/2c^{rab}{A}^{a}d{A}^b$, with $c^r$ matrices that may not be simultaneously diagonalized. We show that these couplings can be related to Green-Schwarz terms of the form $B^r{c}_r^{ab}{F}^a{F}^b$, and how the complete local Lagrangian, that embodies factorized gauge and supersymmetry anomalies (to be disposed of by fermion loops) is uniquely determined by Wess-Zumino consistency conditions, aside from an arbitrary quartic coupling for the gauginos.

LaTeX file, 10 pages. Some equations, previously written with wrong notations, are corrected

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