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Updated: May 22, 2025
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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
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Villain Action in Lattice Gauge Theory
Ilya Chevyrev1,2, Christophe Garban3,4
1Institut für Mathematik, TU Berlin, 10623 Berlin, Germany.
Journal of Statistical Physics
|March 13, 2025
Summary
Villain interaction in lattice gauge theory is shown to be a limit of Wilson and Manton interactions on a carpet graph. This finding extends to non-Abelian theories like SU(3) and validates the Ginibre inequality for Abelian theories.
Area of Science:
- Theoretical Physics
- High Energy Physics
- Condensed Matter Physics
Background:
- Villain, Wilson, and Manton interactions are key concepts in lattice gauge theory.
- Spin O(N) models exhibit analogous properties with cable graphs.
- The Ginibre inequality is a significant result in statistical mechanics.
Purpose of the Study:
- To demonstrate that Villain interaction in lattice gauge theory arises as a limit of Wilson and Manton interactions.
- To extend this finding to non-Abelian lattice gauge theories, including SU(3).
- To broaden the applicability of the Ginibre inequality to Villain interactions in Abelian lattice gauge theories.
Main Methods:
- Mathematical proof establishing the limit of Wilson and Manton interactions on a 'carpet graph'.
- Extension of the proof to non-Abelian lattice gauge theories.
- Application of the derived framework to the Abelian lattice gauge theory case.
Main Results:
- Villain interaction is proven to be the limit of Wilson and Manton interactions on the carpet graph for lattice gauge theory.
- This relationship holds for non-Abelian theories, specifically SU(3)-lattice gauge theory.
- The validity of the Ginibre inequality is extended to Villain interactions in Abelian lattice gauge theory.
Conclusions:
- The carpet graph provides a unified framework for understanding different lattice gauge interactions.
- The study bridges concepts from spin models and lattice gauge theory.
- This work offers new insights into the mathematical structure and inequalities within lattice gauge theories.
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