Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-07-16
JHEP 0811:029,2008
Physics
High Energy Physics
High Energy Physics - Theory
45 pp. v2: typos corrected. v3,v4: other minor corrections
Scientific paper
10.1088/1126-6708/2008/11/029
We discuss, and propose a solution for, a still unresolved problem regarding the breaking from $\N=2$ super-QCD to $\N=1$ super-QCD. A mass term $W=\mu \Tr \Phi^2 / 2$ for the adjoint field, which classically does the required breaking perfectly, quantum mechanically leads to a relevant operator that, in the infrared, makes the theory flow away from pure $\N=1$ SQCD. To avoid this problem, we first need to extend the theory from $\SU (n_c)$ to $\U (n_c)$. We then look for the quantum generalization of the condition $W^{\prime}(m)=0$, that is, the coincidence between a root of the derivative of the superpotential $W(\phi)$ and the mass $m$ of the quarks. There are $2n_c -n_f$ of such points in the moduli space. We suggest that with an opportune choice of superpotential, that selects one of these coincidence vacua in the moduli space, it is possible to flow from $\N=2$ SQCD to $\N=1$ SQCD. Various arguments support this claim. In particular, we shall determine the exact location in the moduli space of these coincidence vacua and the precise factorization of the SW curve.
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