Anomaly means that: the system has a symmetry at classical level(both discrete and continous), but when we quantize the theory, the system no longer holds the symmetry.

I'm wondering for every anomaly, if we can design a experiment to check? For example, the global chiral anomaly, we can measure the life time of photons when the pi zero particle decays. And for parity anomaly, the corresponding experiment is quantum hall effect. However, currently I don't know how to check the conformal anomaly and the gravitational anomaly. And by the way I'm not sure if the gauge anomaly will cause any physical observable effect.

Thank you very much

Anomaly means that: the system has a symmetry at classical level  (both discrete and continous), but when we quantize the theory, the system no longer holds the symmetry.

I'm wondering for every anomaly, if we can design a experiment to check? For example, the global chiral anomaly, we can measure the life time of photons when the pi zero particle decays. And for parity anomaly, the corresponding experiment is quantum hall effect. However, currently I don't know how to check the conformal anomaly and the gravitational anomaly. And by the way I'm not sure if the gauge anomaly will cause any physical observable effect.