Nambu-Goto action and classical rebits in any signature and in higher dimensions

Abstract

We perform an extension of the relation between the Nambu-Goto action and classical rebits. Of course, the Cayley hyperdeterminant is the key mathematical tool in such generalization. Using the Wick rotation, we find that in four dimensions such a relation can be established no only with the signature (2+2) but also with any signature. We generalize our result to a curved space-time of (2$^{2n}$+2$^{2n}$)-dimensions and (2$^{2n+1}$+2$^{2n+1}$)-dimensions.