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Updated: Jun 7, 2025
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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
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Noninvertible Symmetries, Anomalies, and Scattering Amplitudes
Christian Copetti1, Lucía Córdova2, Shota Komatsu2
1Mathematical Institute, <a href="https://ror.org/052gg0110">University of Oxford</a>, Woodstock Road, Oxford OX2 6GG, United Kingdom.
Physical Review Letters
|November 15, 2024
Summary
Crossing symmetry rules for S matrices are altered in theories with noninvertible symmetries. New rules, derived from fusion categories, accommodate these symmetries and anomalies in 2D gapped phases.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Condensed Matter Physics
Background:
- S matrices describe scattering processes in quantum field theories.
- Integrable models and gapped phases are crucial in understanding quantum systems.
- Noninvertible symmetries and anomalies present challenges to standard theoretical frameworks.
Purpose of the Study:
- To investigate the impact of noninvertible symmetries and anomalies on S matrix crossing symmetry.
- To reconcile S matrix properties with these advanced symmetry concepts in 2D integrable flows.
- To develop a consistent framework for S matrices in theories with noninvertible symmetries.
Main Methods:
- Analysis of S matrices within integrable flows to 2D gapped phases.
- Comparison of bootstrap-derived S matrices with constraints from noninvertible symmetries.
- Development of modified crossing symmetry rules based on fusion categories.
Main Results:
- Standard crossing symmetry is violated in theories with noninvertible symmetries.
- S matrices compatible with noninvertible symmetries follow modified rules dictated by fusion categories.
- These modified rules are applicable to theories exhibiting discrete anomalies.
Conclusions:
- Noninvertible symmetries necessitate a revision of standard S matrix crossing symmetry.
- Fusion categories provide the mathematical framework for these modified rules.
- The findings offer new insights into the structure of quantum field theories with exotic symmetries.
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