Gauge Anomalies and Consistency

The diffeomorphism algebra is the gauge symmetry of classical general relativity. An extension thereof is hence a kind of gauge anomaly, which according to conventional wisdom is fatal for the quantum theory. However, the claim that gauge anomalies are always inconsistent is wrong. Counterexample: the free subcritical string, which can be quantized with a ghost-free spectrum despite its conformal gauge anomaly.

Of course, this does not mean that every theory with a gauge anomaly is consistent. Some are (free subcritical string), others are not (free supercritical string, interacting subcritical string). But if the anomalous theory is consistent, some classical gauge symmetry becomes an ordinary quantum symmetry, which acts on the Hilbert space rather than reducing it (here: conformal symmetry). Conversely, some classical gauge degrees of freedom become physical after quantization (trace of the worldsheet metric).

So the crucial property is unitarity, not triviality. 

<Previous    Next>