Alphabeta MathIib Flux And Charge Quantization
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1 · Prerequisites
Abstract Algebra
- Binary Operations, Monoids, Groups and Subgroups
- Composition Series, the Jordan–Hölder Theorem and Solvable Groups
- Cosets, Index and Lagrange's Theorem
- Divisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation
- Finite Averaging and Character-Theory Prerequisites
- Free Groups and Presentations
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- Free Products and Amalgamation
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- Group Homomorphisms and the Isomorphism Theorems
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- Simple Field Extensions and the Construction of the Complex Numbers
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Algebraic Topology
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Category Theory
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Complex Analysis
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Scheme Theory
Set Theory
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String Theory
- CMP Calabi Yau Threefolds And N2 Data
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Topology
- Applications of the Fundamental Group
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- Compactness
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- Hausdorff via the Diagonal
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- Partitions of Unity and Paracompactness
- Separation Axioms: the Hierarchy
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- The Fundamental Group
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- The Seifert–van Kampen Theorem
- The Topology of Euclidean Space
- Topological Spaces and Continuity
- Uniform Spaces: the Three Definitions
- Urysohn's Lemma and the Tietze Extension Theorem
2 · Logical flowchart
3 · Items
Definition
Type IIB Calabi–Yau orientifold flux background conventions
Postulate
GKP free-period quantization for Type IIB three-form flux
Postulate
GKP source-coupled five-form Bianchi identity
Physics theorem
Compact Type IIB D3 tadpole from the sourced five-form Bianchi identity
Sources
- Steven B. Giddings, Shamit Kachru, and Joseph Polchinski, Hierarchies from Fluxes in String Compactifications, arXiv:hep-th/0105097v2
- Mariana Graña, Flux compactifications in string theory: a comprehensive review, arXiv:hep-th/0509003v3
- Thomas Van Riet and Gianluca Zoccarato, Beginners lectures on flux compactifications and related Swampland topics, arXiv:2305.01722v2
- Shamit Kachru, Michael Schulz, and Sandip Trivedi, Moduli Stabilization from Fluxes in a Simple IIB Orientifold, arXiv:hep-th/0201028v2
- Shamit Kachru, Michael B. Schulz, Prasanta K. Tripathy, and Sandip P. Trivedi, New Supersymmetric String Compactifications, arXiv:hep-th/0211182v1
- Michael B. Schulz, Calabi-Yau Duals of Torus Orientifolds, arXiv:hep-th/0412270v4