Symmetry Breaking in SU(2) and Calabi-Yau Constraints on Quantum Gravity — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: SU(2) representation theory underpins spin/weak-force symmetry; its irreducible representations are indexed by half-integers, with adjoint rep dimension 3 (isomorphic to so(3)); center symmetry breaking in Calabi-Yau compactifications constrains higher-form global symmetries in quantum gravity. | MATH: SU(2) irreps labeled by spin j = 0, 1/2, 1, …, dimension 2j+1. Adjoint rep: j=1, dimension 3, generators Ta = 1/2σa (Pauli) in fundamental; structure constants ϵabc (so(3) isomorphism). Center Z(SU(2)) = {± I} ≅ ℤ2. Casimir: C2 = j(j+1). For j=1/2: C2 = 3/4 = 0.75. For j=1: C2 = 2. Clebsch-Gordan: j1 ⊗ j2 = ⨁J=|j1−j2|j1+j2 J. Calabi-Yau: center symmetry breaking criterion involves ℤN (or ℤ2 for SU(2)) higher-form symmetries; quantitative bound from arXiv:2503.19628v1 (no explicit equation extracted from abstract, but inv
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026symmetry,
title = {{Symmetry Breaking in SU(2) and Calabi-Yau Constraints on Quantum Gravity — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658319},
url = {https://zenodo.org/records/23658319},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry Breaking in SU(2) and Calabi-Yau Constraints on Quantum Gravity — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658319
UR - https://zenodo.org/records/23658319
AB - FINDING: SU(2) representation theory underpins spin/weak-force symmetry; its irreducible representations are indexed by half-integers, with adjoint rep dimension 3 (isomorphic to so(3)); center symmetry breaking in Calabi-Yau compactifications constrains higher-form global symmetries in quantum gravity. | MATH: SU(2) irreps labeled by spin j = 0, 1/2, 1, …, dimension 2j+1. Adjoint rep: j=1, dimension 3, generators T^a = 1/2σ^a (Pauli) in fundamental; structure constants ϵ^abc (so(3) isomorphism). Center Z(SU(2)) = {± I} ≅ ℤ_2. Casimir: C_2 = j(j+1). For j=1/2: C_2 = 3/4 = 0.75. For j=1: C_2 = 2. Clebsch-Gordan: j_1 ⊗ j_2 = ⨁_J=|j_1−j_2|^j_1+j_2 J. Calabi-Yau: center symmetry breaking criterion involves ℤ_N (or ℤ_2 for SU(2)) higher-form symmetries; quantitative bound from arXiv:2503.19628v1 (no explicit equation extracted from abstract, but inv Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -