Mathematics – Logic
Scientific paper
Jan 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cqgra..21..337f&link_type=abstract
Classical and Quantum Gravity, Volume 21, Issue 1, pp. 337 (2004).
Mathematics
Logic
1
Scientific paper
In this paper we classified the smooth supersymmetric Kaluza-Klein reductions of the purely gravitational half-BPS backgrounds of M-theory: the purely gravitational plane wave and the Kaluza-Klein monopole. The analysis of the Kaluza-Klein monopole yielded seven possible Kaluza-Klein reductions labelled (A)-(G). In truth, we failed to discard two of the reductions: those labelled (F) and (G). These reductions fail to be smooth due to the fact that the orbits of the Killing vector effecting the reduction have different topological type: at those points where the null rotation component vanishes, the orbits are circles, whereas at the other points they are diffeomorphic to the real line. In other words, although the action is free, some points (corresponding to the circular orbits) possess nontrivial stabilizers: namely the infinite cyclic subgroup generated by the period. A similar argument has already been used in [1] to discard one of the possible reductions of the M2 brane.
Even though the discarded reductions exist, and some of them can even be supersymmetric, one of the purposes of the paper was to present a full classification of smooth reductions of the purely gravitational half-BPS backgrounds of M-theory. As a result the following changes must be made. At the very end of section 3.2, the two cases (F) and (G) must be deleted. In section 3.3, the paragraphs discussing the supersymmetry of these reductions should be omitted. Similarly the entries in table 7 which are in parentheses should also be omitted. In section 3.4, the parameter β in the expression for λ in the unnumbered equation preceding (3.14) should be put to zero, with the corresponding change in equation (3.14). Finally the entry in table10 containing the nullbrane (N) disappears.
References
[1] Figueroa-O'Farrill J and SimA~3n J 2002 Supersymmetric Kaluza-Klein reductions of M2 and M5-branes Adv. Theor. Math. Phys. 6 703-93 (Preprint hep-th/0208107)
Figueroa-O'Farrill José
Simon Jonathan
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