A Coincidence Problem: How to Flow from N=2 SQCD to N=1 SQCD

TL;DR

This paper investigates how to smoothly transition from N=2 to N=1 super-QCD by selecting specific vacua in the moduli space, addressing a longstanding problem with quantum effects altering the classical breaking mechanism.

Contribution

It proposes a method to achieve the N=2 to N=1 flow by choosing particular superpotentials and vacua, extending the gauge group to U(n_c), and identifying coincidence points in the moduli space.

Findings

Identified the exact location of coincidence vacua in the moduli space.

Determined the factorization of the Seiberg-Witten curve at these vacua.

Supported the flow from N=2 to N=1 SQCD with theoretical arguments.

Abstract

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.