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Updated: May 23, 2025
06:35
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
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Higher Structure of Chiral Symmetry.
Christian Copetti1,2, Michele Del Zotto3,4, Kantaro Ohmori5
1Theoretical Particle Physics, SISSA, Via Bonomea, 34124 Trieste, Italy.
Communications in Mathematical Physics
|March 10, 2025
Summary
Non-invertible symmetries in quantum field theory exhibit unique fusion rules, deviating from standard group structures. This study explores their associativity, revealing F-symbols valued in lower-dimensional topological field theories (TFTs).
Area of Science:
- Quantum Field Theory
- High-Energy Physics
- Theoretical Physics
Background:
- Familiar gauge theories in dimensions greater than two can possess non-invertible symmetries.
- These symmetries are generated by topological defects and feature fusion rules with coefficients in topological field theories (TFTs), not just numbers.
Purpose of the Study:
- To explore the associativity structure of non-invertible symmetries in higher dimensions.
- To analyze the F-symbols, which represent the first layer of associativity for these symmetries.
Main Methods:
- Investigate F-symbols, finding they are valued in TFTs one dimension lower than the defect.
- Explicitly analyze F-symbols for the non-invertible chiral symmetry in massless QED.
- Probe F-symbol TFTs using correlators of topological defects with 't Hooft lines.
Main Results:
- F-symbols for non-invertible symmetries are shown to take values in lower-dimensional TFTs.
- Demonstrated that these F-symbol TFTs are detectable via correlators of topological defects and 't Hooft lines.
- Derived the Ward-Takahashi identity for chiral symmetry on four-dimensional manifolds directly from topological defect data.
Conclusions:
- The study establishes a framework for understanding associativity in non-invertible symmetries.
- Provides a method to detect and analyze these symmetries and their associated TFTs.
- Offers a Lagrangian-independent derivation of Ward-Takahashi identities from topological data.
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