Two-dimensional gauge anomalies and $p$-adic numbers

Ben Gripaios; Imogen Camp; Khoi Le Nguyen Nguyen

Two-dimensional gauge anomalies and $p$-adic numbers

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arxiv 2403.10611 v2 pith:6IH37PQ2 submitted 2024-03-15 hep-th hep-ph

Imogen Camp , Ben Gripaios , Khoi Le Nguyen Nguyen This is my paper · ORCID

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keywords solutionsadmitanomaliesanomalygaugeabelianadicadics

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abstract

We show how methods of number theory can be used to study anomalies in gauge quantum field theories in spacetime dimension two. To wit, the anomaly cancellation conditions for the abelian part of the local anomaly admit solutions if and only if they admit solutions in the reals and in the $p$-adics for every prime $p$ and we use this to build an algorithm to find all solutions.

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Anomaly cancellation for two $U(1)$ factors
hep-th 2026-07 accept novelty 7.0 of 10

Abelian anomaly cancellation for rank-K U(1) summands equates to finding (K-1)-planes on a cubic hypersurface over Q; for K=2 and six fermions this is the Fano surface of the Segre cubic, whose rational components ful...

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