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