What question did this study set out to answer?

The aim is to explore how gauge symmetries in the Standard Model can emerge from Hopf-soliton topology within Energy String Field Theory.

March 24, 2026Open Access

Emergent gauge symmetry from Hopf soliton topology in ESFT

Key Points

The aim is to explore how gauge symmetries in the Standard Model can emerge from Hopf-soliton topology within Energy String Field Theory.
Derivation of SU(2) weak isospin from the rotational zero modes of a hedgehog soliton.
Analysis of SU(3) color arising from the permutation symmetry of the rank-3 Hopf-soliton sector.
Identification of U(1) from the residual outer phase field.
Connection to calculations involving Casimir scaling and glueball-spectrum estimates.
Establishment of relationships between Hopf solitons and Standard Model gauge symmetries.
Quantitative results on Casimir scaling and glueball spectrum constraints suggest further gauge sectors.

Abstract

This preprint develops the emergence of the Standard Model gauge structure from Hopf-soliton topology in Energy String Field Theory (ESFT). The manuscript derives SU(2) weak isospin from the rotational zero modes of a single hedgehog soliton, SU(3) color from the permutation symmetry of the rank-3 Hopf-soliton sector, and U(1) from the residual outer phase field. The same framework is further connected to quantitative results including Casimir scaling, glueball-spectrum estimates, and constraints on additional gauge sectors. This version is released as a public preprint for citation and scholarly reference.

Emergent gauge symmetry from Hopf soliton topology in ESFT

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Abstract

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