# What does "local composite symmetry" mean in ${\cal N}=8$ $d=5$ supergravity?

What does it mean "local composite symmetry" in supergravity? Specifically, I don't understand very well the local composite symmetry ${\rm USp}(8)$ in ${\cal N}=8$ $d=5$ supergravity.

• In which reference and in which context does this notion occur? Commented Feb 7, 2015 at 14:57
• In the "COMPACT AND NON-COMPACT GAUGED SUPERGRAVITY THEORIES IN FIVE DIMENSIONS" and in many other references:" The ungauged N = 8 supergravity theory in five dimensions has one graviton, eight symplectic Majorana gravitini, 27 (abelian) vector fields, 48 symplectic Majorana spinors and 42 scalar fields. The theory has a composite local USp(8) symmetry, and a global E6(6) symmetry. " Commented Feb 7, 2015 at 16:47
• This seems to be the paper mentioned above, but cannot tell for sure as I don't have access. @Andrea89: It might be better for you to copy the relevant content of the paper (with link to source, of course) into your post, as ACuriousMind suggested. Commented Feb 7, 2015 at 18:44
• The relevant content of the paper is that i've just written, the rest of the article i think is not useful for answer to question, however i don't understand how i could link the source if it's protected by log in. Commented Feb 7, 2015 at 19:45

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 $SL(6,\mathbb{R})\subseteq E_{6(6)}$.