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.
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1$\begingroup$ In which reference and in which context does this notion occur? $\endgroup$– ACuriousMind ♦Commented Feb 7, 2015 at 14:57
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$\begingroup$ 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. " $\endgroup$– Andrea89Commented Feb 7, 2015 at 16:47
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1$\begingroup$ 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. $\endgroup$– Kyle KanosCommented Feb 7, 2015 at 18:44
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$\begingroup$ 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. $\endgroup$– Andrea89Commented Feb 7, 2015 at 19:45
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1 Answer
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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:
- M. Gunaydin, L.J. Romans and N.P. Warner, Compact and non-compact gauged supergravity theories in five dimensions, Nucl. Phys. B272 (1986) 598.
answered Feb 8, 2015 at 20:15