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Supersymmetry, Vacuum Statistics, and the Fundamental Theorem of Algebra

Donald Spector
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Abstract

I give an interpretation of the fundamental theorem of algebra based on supersymmetry and the Witten index. The argument gives a physical explanation of why a real polynomial of degree $n$ need not have $n$ real zeroes, while a complex polynomial of degree $n$ must have $n$ complex zeroes. This paper also addresses in a general and model-independent way the statistics of the perturbative ground states (the states which correspond to classical vacua) in supersymmetric theories with complex and with real superfields.

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Donald Spector. 1995-07-19. Supersymmetry, Vacuum Statistics, and the Fundamental Theorem of Algebra. https://doi.org/10.1007/bf02102428

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