Abstract
We study in detail how four-dimensional local anomalies manifest themselves when the theory is compactified on a circle. By integrating out the Kaluza-Klein modes in a way that preserves the four-dimensional symmetries in the UV, we show that the three-dimensional theory contains field-dependent Chern-Simons terms that appear at one-loop. These vanish if and only if the four-dimensional anomaly is canceled, so the anomaly is not lost upon compactification. We extend this analysis to situations where anomalies are canceled through a Green-Schwarz mechanism. We then use these results to show automatic cancellation of local anomalies in F-theory compactifications that can be obtained as a limit of M-theory on a smooth Calabi-Yau fourfold with background flux.
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Corvilain, P., Grimm, T.W. & Regalado, D. Chiral anomalies on a circle and their cancellation in F-theory. J. High Energ. Phys. 2018, 20 (2018). https://doi.org/10.1007/JHEP04(2018)020
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DOI: https://doi.org/10.1007/JHEP04(2018)020