Temperature Dependence of the CP N‐1 Model and the Analogy with Quantum Chromodynamics

The two‐dimensional CP N ‐1 model — a simple field‐theoretic analogue of four‐dimensional quantum chromodynamics (QCD) — is analysed and reviewed. The major themes are the temperature dependence of the CP N ‐1 model, and the analogy between CP N ‐1 and QCD. A detailed treatment of the 1/ N approximation of the CP N ‐1 model is given. The main results emerging from this approximation are discussed at length. These are: asymptotic freedom, dimensional transmutation, confinement and topological charge nonquantization at zero temperature T = O, screening and topological charge quantization at finite temperature T . The analogy with QCD is explained in detail. A new, qualitative, analysis of the CP N ‐1 model at finite temperature is introduced. This approach exploits the conformal invariance of the model to “heat” an arbitrary CP N ‐1 field from T = O to finite temperature. This is achieved by conformal‐transforming the flat Euclidean space‐time of the T = O theory to the cylindrical space‐time of the finite temperature theory.