# Baryonic operators in ${\cal N}=1$ $U(N)$ SQCD in four dimensions

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Seiberg's duality is usually considered as a duality for $SU(N_c)$ theories with $N_f$ flavors. In his case, the vacuum for $N_f \geq N_c$ is parameterized by mesons $M$ and baryons ${\bar B}$ and $B$. For example when $N_f = N_c$ the quantum constraint is

$\det M - {\bar B} B = \Lambda^{N}$

If we consider gauge group to be $U(N_c)$ thinking of it as gauging the baryon symmetry of the theory, we can still form gauge invariant operators ${\bar B}B$. However single baryons is not gauge invariant.

Does such baryon ${\bar B}B$ still exists in the vacuum moduli space? There seems to be contradiction in the literature:

In this paper, they considered such operators: http://arxiv.org/pdf/0705.3811v2.pdf

However in the paper of Seiberg, this operator is excluded in the chiral ring: http://arxiv.org/pdf/hep-th/0212225.pdf

Which one is actually correct?

asked Jan 9, 2016

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