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crated D'Auria-Fre formulation of supergravity
there is a blog entry to go with this here
expanded the section on "rheonomy"
I went through the entry D’Auria-Fre formulation of supergravity and edited a bunch of links, making them point to all the relevant entries on oo-Chern-Weil theory that we have created since the conception of this entry. Also polished up the notation here and there to bring it in line with what is now “standard” in the rest of the Lab.
i reorganized the entry D’Auria-Fre formulation of supergravity a bit in an attempt to polish it. Then I added a section on the “cosmo-cocycle”-condition and how it really defines a Chern-Simons element in the supergravity Lie 6-algebra.
Finally I added a stub section “Examples” where I started writing out the cs-element = Lagrangian for 11d-supergravity, before running out of steam.
I have expanded the Idea section a bit, making the relation to higher Cartan geometry explicit (which is being mentioned in a bunch of nLab entries, but had previously not been added to this relatively old entry itself)
when the $n$Lab is back, the entry D’Auria-Fre formulation of supergravity needs to be added a pointer to
which, while not as detailed as the original Supergravity and Superstrings - A Geometric Perspective, includes discussion of new developments such as AdS/CFT in the special D’Auria-Fre formulation – also it’s still in print.
added pointer to today’s review
added pointer to today’s
added pointer to today’s:
added pointer to today’s
finally added pointer to:
added pointer to:
added pointer to:
Yuval Ne’eman, Tullio Regge, Gravity and supergravity as gauge theories on a group manifold, Physics Letters B 74 1–2 (1978) 54-56 [doi:10.1016/0370-2693(78)90058-8, spire:6328]
also: Rivista del Nuovo Cimento 1 5 (1978) 1–43
added pointer to:
In Dec 2018 (revision 72) I had spelled out in the entry the argument for the rheonomy principle from CDF91 III.3, noticing at the end that there is a gap in the argument, since the RHS of the differential equation III.3.29 (p. 653) depends on $d \theta^{\overline{\alpha}}$ not only through a contracted curvature, but also through a contracted vielbein field $\mu_{\overline{\alpha}}$.
Back then I had concluded with a paragraph indicating how this gap might be fixed.
But revisiting the story now, I don’t think this can be fixed in generality, and I have now deleted my paragraph suggesting otherwise.
It looks to me like the concluding sentence below their (III.3.29) is wrong as stated, it forgets about the dependence on $\mu_{\overline{\alpha}}^B(x,0)$ evidently present in the line before, which is not given by the initial value data.
Nevertheless, in the cases of interest things work out, one just needs a more careful argument…
added pointer to further original articles:
Riccardo D’Auria, Pietro Fré, About bosonic rheonomic symmetry and the generation of a spin-1 field in $D=5$ supergravity, Nuclear Physics B 173 3 (1980) 456-476 [doi:10.1016/0550-3213(80)90013-9]
Pietro Fré, Extended supergravity on the supergroup manifold: $N=3$ and $N=2$ theories, Nuclear Physics B 186 1 (1981) 44-60 [doi:10.1016/0550-3213(81)90092-4]
Riccardo D’Auria, Pietro Fré, A. J. da Silva, Geometric structure of $N=1$, $D=10$ and $N=4$, $D=4$ super Yang-Mills theory, Nuclear Physics B 196 2 (1982) 205-239 [doi:10.1016/0550-3213(82)90036-0]
added these pointers:
Riccardo D’Auria, Pietro Fré, Tullio Regge, Geometrical formulation of supergravity as a theory on a supergroup manifold, contribution to Supergravity Workshop, Stony Brook (1979) 85-92 [inspire:148583]
Riccardo D’Auria, Pietro Fré, Tullio Regge, Supergravity and Cohomology Theory: Progress and Problems in $D = 5$, in Unification of the Fundamental Particle Interactions, Ettore Majorana International Science Series, 7 Springer (1980) [doi:10.1007/978-1-4613-3171-1_12]
added also original pointers to the independent formulation of rheonomy via “superspace constraints”:
Warren Siegel, S. James Gates Jr., Superfield supergravity, Nuclear Physics B 147 1–2 (1979) 77-104 [doi:10.1016/0550-3213(79)90416-4]
S. James Gates Jr., Kellogg S. Stelle, Peter C. West Algebraic origins of superspace constraints in supergravity, Nuclear Physics B 169 3–4 (1980) 347-364 [doi:10.1016/0550-3213(80)90037-1]
S. James Gates Jr., On-shell and conformal $N=4$ supergravity in superspace, Nuclear Physics B 213 3 (1983) 409-444 [doi:10.1016/0550-3213(83)90229-8]
added pointer to these early references, which seem to have been overlooked:
N. S. Baaklini, Cartan’s geometrical structure of supergravity, Lett. Math. Phys. 2 (1977) 115-117 [doi:10.1007/BF00398576]
N. S. Baaklini, Spin 3/2 field and Cartan’s geometry, Lett. Math. Phys. 2 (1977) 43-47 [doi:10.1007/BF00420670]
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