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General Solution to the U(1) Anomaly Equations.

Davi B Costa1, Bogdan A Dobrescu2, Patrick J Fox2

  • 1Universidade de São Paulo, São Paulo 05508-090, Brasil.

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|November 9, 2019
PubMed
Summary
This summary is machine-generated.

We solved a complex cubic equation related to U(1) gauge theory and Weyl fermions. Our findings provide a general solution for anomaly cancellation, crucial for theoretical physics models.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Mathematical Physics

Background:

  • Anomaly cancellation is a fundamental requirement in quantum field theories, particularly in the Standard Model.
  • U(1) gauge groups are the simplest non-trivial gauge symmetries, often appearing in extensions of the Standard Model.
  • The existence of Weyl fermions dictates constraints on gauge anomalies.

Purpose of the Study:

  • To solve the Diophantine cubic equation arising from U(1) anomaly cancellation conditions.
  • To provide a general parametrization for charges of Weyl fermions in U(1) gauge theories.
  • To establish the most general solution for anomaly cancellation in this context.

Main Methods:

  • Formulating the anomaly cancellation equations as a Diophantine cubic equation.
  • Developing a parametrization for integer solutions.
  • Proving the general validity of the derived parametrization.

Main Results:

  • The anomaly cancellation equations for U(1) gauge groups are shown to be a cubic equation in n-1 integer variables.
  • A general solution is provided by parametrizing charges in terms of n-2 integers.
  • The derived parametrization is proven to represent the most general solution.

Conclusions:

  • The study presents a complete and general solution to the problem of U(1) anomaly cancellation.
  • The findings offer a powerful tool for constructing consistent theoretical models with U(1) gauge symmetries.
  • This work simplifies the analysis of anomalies in theories with multiple Weyl fermions.