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Calculation of the Witten index in extended supersymmetric Yang-Mills theory

Andrei V. Smilga

Abstract

We calculate the Witten index in N = 2 and N = 4 extended supersymmetric Yang-Mills theories with the gauge group SU(2). The result of the calculation is I/sub W/ = 2 for the N = 2 theory and I/sub W/ = 10 for the N = 4 theory. The nonzero value of I/sub W/ indicates that there is no spontaneous supersymmetry breaking in these theories.

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Key concepts: Yang–Mills theory, Gauge group, Supersymmetry, Mathematical physics, Gauge theory, Supersymmetric gauge theory, Physics, Supersymmetry breaking