No zero energy states for the supersymmetric x(2)y(2) potential

• We show that the positive supersymmetric matrix-valued differential operator H = p(x)(2) + p(y)(2) + x(2)y(2) + xsigma(3) + ysigma(1) has no zero modes, i.e., Hpsi = 0 implies psi = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang Mills theories.

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supersymmetric matrix models

zero modes

matrix models

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