Scaling behaviour of conformal fields in curved three-dimensional space

The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theoryʹs scaling behaviour reveals that scalar-loop effects contribute to the conformal anomaly only at advanced orders allowing for a range of relevant energy scales which extend to those comparable to the non-perturbative scale of Planck mass.