Specifically, the word *composite* refers to a composed form of the ${\rm USp}(8)$ connection $Q_{\mu a}{}^{b}$. It depends on a vielbein $V_{ABab}$ and a connection $A_{\mu IJ}$, see eq. (4.3) in Ref. 1 for details.

Here the index $\mu$ is a 5-dimensional spacetime index; the indices $AB$ refer to the $\bar{\bf 27}$ of $E_{6(6)}$; the indices $ab$ refer to the ${\bf 27}$ of ${\rm USp}(8)\subseteq E_{6(6)}$; the indices $IJ$ refer to $SL(6,\mathbb{R})\subseteq E_{6(6)}$.

References:

- M. Gunaydin, L.J. Romans and N.P. Warner,
*Compact and non-compact gauged supergravity theories in five dimensions,* Nucl. Phys. B272 (1986) 598.

This post imported from StackExchange Physics at 2015-02-10 11:06 (UTC), posted by SE-user Qmechanic