  A general mechanism for the loss of conformal invariance is the merger and
disappearance of an infrared fixed point and an ultraviolet fixed point of a
renormalization group flow. We show explicitly how this mechanism works in the
case of identical bosons at unitarity as the spatial dimension $d$ is varied.
For $d$ between the critical dimensions $d_{\rm 1}=2.30$ and $d_{\rm 2}=3.76$,
there is loss of conformality as evidenced by the Efimov effect in the
three-body sector. The beta function for an appropriate three-body coupling is
a quadratic polynomial in that coupling. For $d<d_{\rm 1}$ and for $d>d_{\rm
2}$, the beta function has two real roots that correspond to infrared and
ultraviolet fixed points. As $d$ approaches $d_{\rm 1}$ from below and as $d$
approaches $d_{\rm 2}$ from above, the fixed points merge and disappear into
the complex plane. For $d_{\rm 1}<d<d_{\rm 2}$, the beta function has complex
roots and the renormalization group flow for the three-body coupling is a limit
cycle.
