Vev of Energy momentum tensor and $\beta-$ function in a supersymmetric QFT

Question

We know that if a gauge theory runs then the vev of the (trace of) energy momentum tensor is proportional to (possibly sum of) beta function of the gauge couplings. In a supersymmetric gauge theory however, on a SUSY preserving vacuua we know that the vev of trace of the energy momentum tensor is zero (by SUSY algebra).

This argument seems to imply that a non-conformal supersymmetric gauge theory does not exhibit any SUSY preserving vacuua!!

This is clearly far from the truth. Massless SQCD for example has non-zero beta function for the gauge coupling $\propto 3N_c-N_f$ but still admits a rich moduli space of vacuua.

Where is the argument going wrong?

This post imported from StackExchange Physics at 2015-01-22 11:40 (UTC), posted by SE-user Orbifold

Comments

The trace of the stress tensor is proportional to the beta function and the vev of another operator, the gluon condensate. Obviously, the gluon condensate can vanish even if the beta function does not.