  We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass
deformations of N=4 SYM, and investigate how the backreaction of the RR and
NS-NS two-form potentials dual to the fermion masses contribute to
Coulomb-branch potential of D3 branes, which we interpret as the bulk boson
mass matrix. Using representation-theory and supergravity arguments we show
that the fermion masses completely determine the trace of this matrix, and that
on the other hand its traceless components have to be turned on as
non-normalizable modes. Our result resolves the tension between the belief that
the AdS bulk dual of the trace of the boson mass matrix (which is not a chiral
operator) is a stringy excitation with dimension of order $(g_s N)^{1/4}$ and
the existence of non-stringy supergravity flows describing theories where this
trace is nonzero, by showing that the stringy mode does not parameterize the
sum of the squares of the boson masses but rather its departure from the trace
of the square of the fermion mass matrix. Hence, asymptotically-AdS flows can
only describe holographically theories where the sums of the squares of the
bosonic and fermionic masses are equal, which is consistent with the
weakly-coupled result that only such theories can have a conformal UV fixed
point.
