Timeline for Induced "ungauged" Chern-Simons terms from a massive Dirac fermion
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2020 at 15:54 | comment | added | Buzz♦ | @Aaron My point is that, because the theory is still gauge invariant, those terms automatically do not appear. | |
| Apr 4, 2020 at 4:34 | comment | added | Aaron | The reason why I am trying to explicitly differentiate between gauge theory vs (ungauged) local symmetry is that it is commonly said that the massless Dirac fermion has a parity anomaly enforced on it because the regularization (via a mass term) must preserve gauge invariance. On the face, I agree with you that it doesn't matter if the theory is gauged or not, but relevant terms such as a $mA^2$ become allowed if the theory is not gauged, so I don't know the fate of the IR theory. | |
| Apr 4, 2020 at 2:05 | comment | added | Buzz♦ | @Aaron You seem to be trying to make a distinction that does not really exist, between an "explicit" gauge symmetry and a theory that merely possesses a gauge symmetry. Any theory with a gauge-invariant action is really a gauge theory, unless the matter sector is such that the regularization cannot preserve the gauge symmetry (that is, when there is a gauge anomaly), in which case the theory is generally inconsistent. | |
| Apr 3, 2020 at 14:35 | comment | added | Aaron | My question is not asking whether or not Chern-Simons theory is gauge invariant, but whether to what extent the explicit gauging of the theory, namely enforcing the gauge symmetry of the theory, affects the renormalization flow. Does the Chern-Simons term still dominate even in the IR limit if the theory is not gauged? | |
| Apr 2, 2020 at 19:11 | history | answered | Buzz♦ | CC BY-SA 4.0 |