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Oct 30, 2019 at 9:33 comment added Prof. Legolasov @SvenForkbeard the interpretation from the path integral point of view is quite interesting, and very similar to the toy model with the axion. You start with the Polyakov path integral and observe that the measure isn't invariant under conformal transformations leading to the conformal anomaly. This can be re-interpreted as a non-invariance of the auxiliary term in the action (the Liouville action). This paper seems to do a good job at explaining this: iopscience.iop.org/article/10.1209/0295-5075/7/8/009
Oct 30, 2019 at 9:22 comment added SvenForkbeard Thanks, this is an interesting example. It's not clear to me how one should interpret this from a path integral point of view (although this is not too problematic for me). Can we give other examples then, in addition to this, where there is a very clear path integral expression where the transformation of the measure cancels precisely with the change in the action?
Oct 30, 2019 at 7:34 history answered Prof. Legolasov CC BY-SA 4.0