Supersymmetry, Vacuum Statistics, and the Fundamental Theorem of Algebra

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.

arXiv comment18 pages, harvmac. The revisions provide a more detailed discussion of the mathematical context of the results

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