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

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

$$\det M - {\bar B}B = \Lambda^{2N_c}$$

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/abs/0705.3811v2

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

Which one is actually correct?