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We establish a connection between oriented matroid theory and loop quantumgravity in (2+2) (two time and two space dimensions) and 8-dimensions. We startby observing that supersymmetry implies that the structure constants of thereal numbers, complex numbers, quaternions and octonions can be identified withthe chirotope concept. This means, among other things, that normed divisionsalgebras, which are only possible in 1,2, 4 or 8-dimensions, are linked tooriented matroid theory. Therefore, we argue that the possibility fordeveloping loop quantum gravity in 8-dimensions must be taken as importantalternative. Moreover, we show that in 4-dimensions, loop quantum gravitytheories in the (1+3) or (0+4) signatures are not the only possibilities. Infact, we show that loop quantum gravity associated with the (2+2)-signature mayalso be an interesting physical structure.

Oriented matroid theory and loop quantum gravity in (2+2) and eight dimensions