We consider back-reaction by non-supersymmetric D7/anti-D7 probe branes in
the Kuperstein-Sonnenschein model at finite temperature. Using the smearing
technique, we obtain an analytical solution for the back-reacted background to
leading order in N_f/N_c. This back-reaction explicitly breaks the conformal
invariance and introduces a dimension 6 operator in the dual field theory which
is an irrelevant deformation of the original conformal field theory. We further
probe this back-reacted background by introducing an additional set of probe
brane/anti-brane. This additional probe sector undergoes a chiral phase
transition at finite temperature, which is absent when the back-reaction
vanishes. We investigate the corresponding phase diagram and the thermodynamics
associated with this phase transition. We also argue that additional probes do
not suffer from any instability caused by the back-reaction, which suggests
that this system is stable beyond the probe limit.Comment: 56 pages, 8 figures. References updated, improved discussion on
dimension eight operato