# 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? – ACuriousMind Feb 7 '15 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. " – Andrea89 Feb 7 '15 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. – Kyle Kanos Feb 7 '15 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. – Andrea89 Feb 7 '15 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 $SL(6,\mathbb{R})\subseteq E_{6(6)}$.