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Supersymmetry O'Raifeartaigh model negative fermionic masses

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Jan27-08, 12:40 PM
P: 4

I calculated a basic O'Raifeartaigh model, using the following potential
[tex] f = \lambda Y_1 (X^2 - M^2) + \mu Y_2 X [/tex], where [tex]Y_1[/tex], [tex]Y_2[/tex] and [tex]X[/tex] are chiral superfields. Assuming that the vacuum expectation value of [tex]y_1[/tex] is zero (where [tex]y_1[/tex] is the scalar component of [tex]Y_1[/tex]), I get a fermionic mass matrix like
\left(\begin{array}{ccc}0 & 0 & 0 \\0 & 0 & \mu \\0 & \mu &0\end{array}\right)[/tex].

My problem is that the eigenvalues of this fermionic mass matrix are [tex]\mu[/tex] and [tex]-\mu[/tex], and I dont understand the later. Why do I get a negative mass and how can I interpet it?

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