I What are anomalies in quantum field theory?

[KleinMoretti]

from the little i understand there are certain symmetries that are broken in quantum field theory, i also know that gauge symmetries must cancel in order to avoid inconsistencies in the theory.

if gauge anomalies need to be cancelled does that mean they dont correspond to a physical non-conserved current and if that's the case what about a chiral anomaly which does correspond to a physical non-conserved current?

 

[PeterDonis]

Moderator's note: Thread title edited for clarity.

 

[Demystifier]

if gauge anomalies need to be cancelled does that mean they dont correspond to a physical non-conserved current and if that's the case what about a chiral anomaly which does correspond to a physical non-conserved current?

Gauge "symmetries" don't correspond to conserved currents, to begin with, irrespective of anomalies. Chiral symmetry is not a gauge symmetry.

 

[haushofer]

from the little i understand there are certain symmetries that are broken in quantum field theory, i also know that gauge symmetries must cancel in order to avoid inconsistencies in the theory.

if gauge anomalies need to be cancelled does that mean they dont correspond to a physical non-conserved current and if that's the case what about a chiral anomaly which does correspond to a physical non-conserved current?

My 2 cents: anomalies concerning gauge symmetries (or better: gauge redundancies) are all about degrees of freedom. In QED you start out classically with a spin-1 field having 2 physical degrees of freedom, and after quantization you want to keep it that way. That means you want to retain the gauge symmetry. If an anomaly breaks this gauge symmetry suddenly the amount of degrees of freedom would change, and we have no idea what that means in the original scheme of quantization.

The same goes for e.g. string theory. In the Polyakov-formulation you start out with conformal symmetry. That symmetry garantuees that the worldsheet metric can be gauge fixed completely. After quantization you want to keep that conformal symmetry, because otherwise the metric would obtain a degree of freedom which you don't know how to interpret.

 

[Demystifier]

If an anomaly breaks this gauge symmetry suddenly the amount of degrees of freedom would change, and we have no idea what that means in the original scheme of quantization.

The main problem with breaking of gauge symmetry is that the resulting theory is no longer unitary. In older literature it is argued that the main problem is non-renormalizability, but this is not such a big problem if we take the point of view that all theories are just effective theories after all, so they don't need to be renormalizable.