Recognition: 2 theorem links
· Lean TheoremGeneralizations and UV completions of Cho-Maison monopole
Pith reviewed 2026-05-11 01:43 UTC · model grok-4.3
The pith
Cho-Maison monopoles arise in many gauge theories and serve as the low-energy description of larger monopoles in extended models.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We explicitly construct Cho-Maison-like monopole configurations in a broad class of models and embed the Cho-Maison monopole as the low-energy effective description of an 't Hooft-Polyakov monopole. In the Pati-Salam model, a monopole reduces to the electroweak Cho-Maison monopole once heavier degrees of freedom are integrated out.
What carries the argument
The Cho-Maison monopole configuration, whose singular core is supported by electroweak-type symmetry breaking, and its embedding as the infrared limit inside an 't Hooft-Polyakov monopole after integrating out heavy fields.
Load-bearing premise
The essential structure of the Cho-Maison monopole relies on an electroweak-type symmetry breaking pattern that can be realized in other gauge theories.
What would settle it
Explicit construction of a monopole solution in the Pati-Salam model that fails to reduce to the Cho-Maison form once fields heavier than the electroweak scale are integrated out.
read the original abstract
A monopole configuration in the electroweak theory was constructed by Cho and Maison, allowing for a singular behavior at the origin. Since the essential structure of the Cho-Maison monopole is based on an electroweak-type symmetry breaking, similar monopole configurations are expected to arise more generally in gauge theories containing such a structure. In this paper, we explicitly show that Cho-Maison-like monopole configurations can indeed be constructed in a broad class of models. We also show that the Cho-Maison monopole can be embedded into an 't Hooft-Polyakov monopole as its low-energy effective description. In particular, we find that a monopole in the Pati-Salam model behaves as the electroweak Cho-Maison monopole once degrees of freedom which are heavier than the electroweak scale are integrated out.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper generalizes the Cho-Maison monopole from the electroweak theory to a broad class of gauge theories featuring electroweak-type symmetry breaking. It provides explicit constructions of Cho-Maison-like monopole configurations in these models and demonstrates an embedding of the Cho-Maison monopole as the low-energy effective description of an 't Hooft-Polyakov monopole. A concrete realization is given in the Pati-Salam model, where the monopole reduces to the electroweak Cho-Maison solution after integrating out degrees of freedom heavier than the electroweak scale.
Significance. If the explicit constructions and effective-theory reductions hold, this work supplies a systematic framework for realizing singular monopoles in models with electroweak symmetry breaking and for embedding them in UV completions. The concrete Pati-Salam example and the integration-out procedure constitute a clear strength, offering a falsifiable link between GUT-scale monopoles and their electroweak-scale effective descriptions.
minor comments (1)
- [Abstract] The abstract would benefit from a single sentence listing the other models (beyond Pati-Salam) in which explicit constructions are performed, to immediately convey the breadth of the class.
Simulated Author's Rebuttal
We thank the referee for their positive summary of our manuscript and for recommending acceptance. The referee's description accurately reflects the scope and results of the work.
Circularity Check
No significant circularity; explicit constructions and effective-theory limits are independent
full rationale
The paper's central claims consist of explicit ansatz constructions of Cho-Maison-like monopoles in models with electroweak-type breaking and a standard integration-out procedure showing that the Pati-Salam monopole reduces to the electroweak Cho-Maison solution at low energies. These steps use conventional gauge-theory embeddings and symmetry breaking patterns without reducing to self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations. The derivation chain remains self-contained against external benchmarks and does not invoke uniqueness theorems or ansatzes from prior author work in a circular manner.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Gauge theories containing an electroweak-type symmetry breaking structure admit Cho-Maison-like monopoles.
Lean theorems connected to this paper
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IndisputableMonolith/Foundation/AlexanderDuality.leanalexander_duality_circle_linking unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
The essential structure of the Cho-Maison monopole is based on an electroweak-type symmetry breaking... we explicitly construct a generalized Cho-Maison monopole configuration in a toy model with symmetry breaking SU(3)×SO(3)→SO(3)diag... two gauge patches that are glued together.
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
the Cho-Maison monopole can be embedded into an 't Hooft-Polyakov monopole as its low-energy effective description... after degrees of freedom which are heavier than the electroweak scale are integrated out.
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
Works this paper leans on
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discussion (0)
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