#extradimensions — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #extradimensions, aggregated by home.social.
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🙈 New preprint, Part V: *What the Higgs Potential Cannot See*.
If you build gauge–Higgs unification models: there is a discrete choice you may be scanning over for nothing. On \(T^2/\mathbb{Z}_2\) each bulk multiplet carries boundary signs \(\eta_0,\eta_1\). For a whole class of bulk matter, the product \(\eta=\eta_0\eta_1\) has no observable consequence in the Higgs sector at one loop. Not suppressed. Identically zero.
Why. The one-loop Wilson-line potential is one operator traced twice. Even windings give a graded dimension, odd windings an index:
\[\Sigma_\lambda=s_\lambda(1,1,t,t^{-1}),\qquad D_\lambda=s_\lambda(1,-1,t,t^{-1}),\]
and AHMN's \(\{A+B(-1)^{k_2}\}\) is exactly \((\Sigma\pm D)/2\). \(\Sigma\) has non-negative coefficients and can never cancel; \(D\) can. η multiplies \(D\) and nothing else — so η is invisible exactly where \(D_\lambda\equiv 0\).Which matter is blind is a parity condition you read off the Young diagram: \(\lambda_1\not\equiv\lambda_2\not\equiv\lambda_3\not\equiv\lambda_4\), or \(\lambda_i+\lambda_{5-i}=c\) odd. Counted in closed form — \(\lceil (k+1)^2/2\rceil\) at \(\lambda_1=2k+1\), none for \(\lambda_1\) even — and machine-checked in Lean 4, sorry-free. A second, disjoint cause: only \(\lfloor (N+1)^2/2\rfloor\) of the \((N+1)^2\) boundary-condition classes of \(SU(N)\) have a coset sector at all, for every \(N\).
Anchored, not fitted: twelve printed coefficients of arXiv:2312.08608 come out exactly, and two further published potentials follow from the same mode counts.
📄 https://doi.org/10.5281/zenodo.21727094
💻 https://github.com/karlesmarin/higgs-blind-class#Physics #ParticlePhysics #HEP #BSM #Higgs #ExtraDimensions #Lean4
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🙈 New preprint, Part V: *What the Higgs Potential Cannot See*.
If you build gauge–Higgs unification models: there is a discrete choice you may be scanning over for nothing. On \(T^2/\mathbb{Z}_2\) each bulk multiplet carries boundary signs \(\eta_0,\eta_1\). For a whole class of bulk matter, the product \(\eta=\eta_0\eta_1\) has no observable consequence in the Higgs sector at one loop. Not suppressed. Identically zero.
Why. The one-loop Wilson-line potential is one operator traced twice. Even windings give a graded dimension, odd windings an index:
\[\Sigma_\lambda=s_\lambda(1,1,t,t^{-1}),\qquad D_\lambda=s_\lambda(1,-1,t,t^{-1}),\]
and AHMN's \(\{A+B(-1)^{k_2}\}\) is exactly \((\Sigma\pm D)/2\). \(\Sigma\) has non-negative coefficients and can never cancel; \(D\) can. η multiplies \(D\) and nothing else — so η is invisible exactly where \(D_\lambda\equiv 0\).Which matter is blind is a parity condition you read off the Young diagram: \(\lambda_1\not\equiv\lambda_2\not\equiv\lambda_3\not\equiv\lambda_4\), or \(\lambda_i+\lambda_{5-i}=c\) odd. Counted in closed form — \(\lceil (k+1)^2/2\rceil\) at \(\lambda_1=2k+1\), none for \(\lambda_1\) even — and machine-checked in Lean 4, sorry-free. A second, disjoint cause: only \(\lfloor (N+1)^2/2\rfloor\) of the \((N+1)^2\) boundary-condition classes of \(SU(N)\) have a coset sector at all, for every \(N\).
Anchored, not fitted: twelve printed coefficients of arXiv:2312.08608 come out exactly, and two further published potentials follow from the same mode counts.
📄 https://doi.org/10.5281/zenodo.21727094
💻 https://github.com/karlesmarin/higgs-blind-class#Physics #ParticlePhysics #HEP #BSM #Higgs #ExtraDimensions #Lean4
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“Do you believe the universe has more dimensions than we currently understand?”
Very interesting question. I don’t have a definitive answer, but I can share some of the scientific theories and evidence that explore this possibility/some of the ways we are trying to answer this fascinating question.
Learn more via the links provided in thread. ⬇️
#Universe #ExtraDimensions #Dimensions #Science #TodaysQuestion
-
“Do you believe the universe has more dimensions than we currently understand?”
Very interesting question. I don’t have a definitive answer, but I can share some of the scientific theories and evidence that explore this possibility/some of the ways we are trying to answer this fascinating question.
Learn more via the links provided in thread. ⬇️
#Universe #ExtraDimensions #Dimensions #Science #TodaysQuestion