Geometric general solution to the U(1) anomaly equations

DOI10.1007/JHEP05(2020)065zbMATH Open1437.83123arXiv1912.04804OpenAlexW3100898785MaRDI QIDQ779336

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Publication date: 21 July 2020

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Abstract: Costa et al. [Phys. Rev. Lett. 123, 151601 (2019)] recently gave a general solution to the anomaly equations for $n$ charges in a $U(1)$ gauge theory. `Primitive' solutions of chiral fermion charges were parameterised and it was shown how operations performed upon them (concatenation with other primitive solutions and with vector-like solutions) yield the general solution. We show that the ingenious methods used there have a simple geometric interpretation, corresponding to elementary constructions in number theory. Viewing them in this context allows the fully general solution to be written down directly, without the need for further operations. Our geometric method also allows us to show that the only operation Costa et al. require is permutation. It also gives a variety of other, qualitatively similar, parameterisations of the general solution, as well as a qualitatively different (and arguably simpler) form of the general solution for $n$ even.

Full work available at URL: https://arxiv.org/abs/1912.04804

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