Alphabeta MathCFT Noninvertible Symmetry Defects
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1 · Prerequisites
Abstract Algebra
Category Theory
- Abelian Categories
- Categories, Functors and Natural Transformations
- Duality and Rigidity in Monoidal Categories
- Limits and Colimits
- Monoidal Categories and Monoidal Functors
- Preadditive and Additive Categories and Biproducts
- Reflective Subcategories and the Adjoint Functor Theorems
- Subobject Lattices Generators and the Grothendieck Axioms
- Tensor and Fusion Categories
Combinatorics
Linear Algebra
Quantum Algebra and Representation Theory
Quantum Field Theory Mathematics
Real Analysis
- Construction of the Real Numbers via Cauchy Sequences
- Construction of the Real Numbers via Dedekind Cuts
- Countability and Uncountability
- Foundations of the Real Numbers for Analysis
- Roots, Rational Powers, and Classical Inequalities
- The Formal Laurent Series Field ℝ((t⁻¹)): Cauchy Complete, Non-Archimedean, Not Complete
Set Theory
- Cardinal Arithmetic, Cofinality and the Alephs
- Construction of the Natural Numbers
- Order, Zorn's Lemma, and the Axiom of Choice
- Ordinal Arithmetic and the First Uncountable Ordinal
- Ordinals, Cardinals, and Transfinite Recursion
- Relations, Functions, and Quotients
- The ZFC Axioms and the Basic Set Constructions
2 · Logical flowchart
3 · Items
Definition
Topological defects, interfaces, orientation, and fusion conventions
Definition
Finite-group gauging wall conventions
Physics theorem
Fusion of a normalized finite-group gauging wall with its reverse
Postulate
Adopted compact-boson flat-gauging and rational self-duality model
Physics theorem
Noninvertible T-duality defect for the compact boson
Sources
- Riccardo Argurio et al., Non-Invertible T-duality at Any Radius via Non-Compact SymTFT, arXiv:2409.11822v1
- Paul Ginsparg, Applied Conformal Field Theory, Les Houches 1988, arXiv:hep-th/9108028v1
- Guillermo Arias-Tamargo et al., Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions, arXiv:2605.13952v1
- Riccardo Argurio, Andrés Collinucci, Giovanni Galati, Ondrej Hulik, and Elise Paznokas, Non-Invertible T-duality at Any Radius via Non-Compact SymTFT, arXiv:2409.11822v1
- Pavel Mnev and Nicolai Reshetikhin, Lecture notes on conformal field theory
- Argurio, Galati, and Godechal, Lattice Realizations of Flat Gauging and T-duality Defects at Any Radius, arXiv:2604.09126v1