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

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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.

This post imported from StackExchange Physics at 2015-02-10 11:06 (UTC), posted by SE-user Andrea89
asked Feb 7, 2015
In which reference and in which context does this notion occur?

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

This post imported from StackExchange Physics at 2015-02-10 11:06 (UTC), posted by SE-user Andrea89
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.

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

This post imported from StackExchange Physics at 2015-02-10 11:06 (UTC), posted by SE-user Andrea89

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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:

1. 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
answered Feb 8, 2015 by (2,860 points)

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