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

TL;DR

This paper classifies the most general couplings of abelian vectors and tensors in six-dimensional supergravity, revealing their relation to Green-Schwarz terms and deriving the complete anomaly-canceling Lagrangian via consistency conditions.

Contribution

It provides a comprehensive description of general abelian vector-tensor couplings and their relation to anomaly cancellation in six-dimensional supergravity.

Findings

Couplings relate to Green-Schwarz terms with non-diagonal matrices.

The complete Lagrangian is uniquely determined by anomaly consistency conditions.

The framework accommodates arbitrary gaugino quartic couplings.

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 $H^{r}=d B^{r}-1/2 c^{rab} A^{a}d A^{b}$, 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.