Scaling Behaviour of Conformal Fields in Curved Three-dimensional Space

TL;DR

This paper investigates how conformally invariant scalar fields behave in curved three-dimensional space, revealing that quantum effects contribute to anomalies at higher orders, influencing the theory's behavior near the Planck scale.

Contribution

It provides a detailed analysis of the scaling behavior of conformal fields in 3D curved space, highlighting the order at which quantum anomalies emerge.

Findings

Scalar-loop effects contribute to conformal anomaly at advanced orders

Relevant energy scales extend to near the Planck mass

Quantum effects influence the semi-classical gravity limitations

Abstract

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 theory's 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.