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Physics#Topological Quantum Field Theory, Fermions, Anomalies, Standard Model🔬 ResearchAnalyzed: Jan 3, 2026 06:12

Anomalous TQFTs for Fermionic Systems via Symmetry Extension

Published:Dec 31, 2025 18:36
1 min read
ArXiv

Analysis

This paper investigates nonperturbative global anomalies in 4D fermionic systems, particularly Weyl fermions, focusing on mixed gauge-gravitational anomalies. It proposes a symmetry-extension construction to cancel these anomalies using anomalous topological quantum field theories (TQFTs). The key idea is to replace an anomalous fermionic system with a discrete gauge TQFT, offering a new perspective on low-energy physics and potentially addressing issues like the Standard Model's anomalies.
Reference

“The paper determines the minimal finite gauge group K of anomalous G-symmetric TQFTs that can match the fermionic anomaly via the symmetry-extension construction.”

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Research Paper#Topological Quantum Field Theory, Category Theory🔬 ResearchAnalyzed: Jan 3, 2026 17:05

Coherent 2D TQFTs via Spans and 2-Segal Sets

Published:Dec 31, 2025 14:31
1 min read
ArXiv

Analysis

This paper explores the mathematical structure of 2-dimensional topological quantum field theories (TQFTs). It establishes a connection between commutative Frobenius pseudomonoids in the bicategory of spans and 2-Segal cosymmetric sets. This provides a new perspective on constructing and understanding these TQFTs, potentially leading to advancements in related fields like quantum computation and string theory. The construction from partial monoids is also significant, offering a method for generating these structures.
Reference

“The paper shows that commutative Frobenius pseudomonoids in the bicategory of spans are in correspondence with 2-Segal cosymmetric sets.”

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Physics#Conformal Field Theory, Topological Quantum Field Theory, Duality🔬 ResearchAnalyzed: Jan 3, 2026 16:43

Generalized Level-Rank Duality and Non-Invertible Anyon Condensation in CFT

Published:Dec 30, 2025 19:00
1 min read
ArXiv

Analysis

This paper explores the connections between holomorphic conformal field theory (CFT) and dualities in 3D topological quantum field theories (TQFTs), extending the concept of level-rank duality. It proposes that holomorphic CFTs with Kac-Moody subalgebras can define topological interfaces between Chern-Simons gauge theories. Condensing specific anyons on these interfaces leads to dualities between TQFTs. The work focuses on the c=24 holomorphic theories classified by Schellekens, uncovering new dualities, some involving non-abelian anyons and non-invertible symmetries. The findings generalize beyond c=24, including a duality between Spin(n^2)_2 and a twisted dihedral group gauge theory. The paper also identifies a sequence of holomorphic CFTs at c=2(k-1) with Spin(k)_2 fusion category symmetry.
Reference

“The paper discovers novel sporadic dualities, some of which involve condensation of anyons with non-abelian statistics, i.e. gauging non-invertible one-form global symmetries.”

PermalinkArXiv