Spectral Emergence from Topological Solitons: A Unified Conjecture for Gauge Representations
Abstract
We formulate a unified conjecture: for topological solitons of charge B in a nonlinear field theory, the quantum spectrum on the moduli space MB is given by the class-1 representations of the global symmetry G̃ with respect to the residual stabilizer HB, with admissible representations selected by topological constraints (Finkelstein-Rubinstein sign for SU(2), Wess-Zumino-Witten triality for SU(3)). We verify this conjecture in six cases spanning four qualitative regimes of HB, with quantitative agreements < 1% where data exist. We identify the Hopf fibration as the geometric origin of U(1)EM and propose a concrete program for local gauge emergence via Berry phase holonomy and Hull-Spence gauging of moduli isometries. The η-invariant on the Atiyah-Hitchin manifold (B=2) is identified as a potentially original computation. The moduli structure identified here determines which representations enter the trace of the heat kernel K(τ) = Tr(e−τ 𝒟2); companion papers address the chirality emerging from the UV topological limit (Emergence Paper II [30]) and the baryon masses generated by the full proper-time integral (Emergence Paper III [29]).
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BibTeX
@misc{dechery2026spectral,
title = {{Spectral Emergence from Topological Solitons: A Unified Conjecture for Gauge Representations}},
author = {Fabien Déchery},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05751208v4},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Spectral Emergence from Topological Solitons: A Unified Conjecture for Gauge Representations
AU - Fabien Déchery
PY - 2026
DA - 2026/09/15
PB - HAL
UR - https://hal.science/hal-05751208v4
AB - We formulate a unified conjecture: for topological solitons of charge B in a nonlinear field theory, the quantum spectrum on the moduli space M_B is given by the class-1 representations of the global symmetry G̃ with respect to the residual stabilizer H_B, with admissible representations selected by topological constraints (Finkelstein-Rubinstein sign for SU(2), Wess-Zumino-Witten triality for SU(3)). We verify this conjecture in six cases spanning four qualitative regimes of H_B, with quantitative agreements < 1% where data exist. We identify the Hopf fibration as the geometric origin of U(1)_EM and propose a concrete program for local gauge emergence via Berry phase holonomy and Hull-Spence gauging of moduli isometries. The η-invariant on the Atiyah-Hitchin manifold (B=2) is identified as a potentially original computation. The moduli structure identified here determines which representations enter the trace of the heat kernel K(τ) = Tr(e^−τ 𝒟^2); companion papers address the chirality emerging from the UV topological limit (Emergence Paper II [30]) and the baryon masses generated by the full proper-time integral (Emergence Paper III [29]).
ER -