Abstract
We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO (n, n) symmetry. In the process we discover new type of numbers which we called "complexoids" in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow one to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.
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