  Recently a non-supersymmetric conformal field theory with an exactly marginal
deformation in the large $N$ limit was constructed by
Chaudhuri-Choi-Rabinovici. On a non-supersymmetric conformal manifold, $c$
coefficient of the trace anomaly in four dimensions would generically change.
In this model, we, however, find that it does not change at the first
non-trivial order given by three-loop diagrams.
