Hidden symmetries, central charges and all that

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Abstract
In this review we discuss hidden symmetries of toroidal compactifications of 11-dimensional supergravity. We recall alternative versions of this theory which exhibit traces of the hidden symmetries while still retaining the massive Kaluza-Klein states. We reconsider them in the broader perspective of M-theory which incorporates a more extended variety of BPS states. We also argue for a new geometry that may underlie these theories. All our arguments point towards an extension of the number of spacetime coordinates beyond 11.
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