Parent-Channel Closure for Composite Complex Scalars: A Generic EFT Criterion and an Axis Model Application
Andrew Morton · Public preprint · Conditional scalar-closure criterion
Gives a checkable criterion for several effective descriptions to share one complex scalar field, using a specified parent response spectrum, compact symmetry and a common matching prescription.
Current Suite Reference Guide · Physical source normalization · Ultraviolet matching
Abstract
Complex scalar fields can enter effective field theories as elementary fields, order parameters, auxiliary variables, condensate coordinates, or composite response coordinates. This paper formulates a parent-channel closure criterion for the case in which a one-complex-scalar effective field is claimed to arise from a fixed microscopic scalar coherence channel. The criterion separates four layers: a parent-channel certificate, the minimal faithful representation of a compact charged scalar block, the parent response data fixing the effective coefficients, and the downstream matching maps using those coefficients. The representation-theoretic step is standard: a connected compact U(1) has no nontrivial one-real-dimensional charged representation; its smallest faithful real charged block is two-dimensional, equivalently one complex scalar. The substantive condition is provenance. The parent certificate must select a single compact scalar channel with positive-norm local response, stabilizing higher response data, an effective cutoff, and no additional light charged scalar block below that cutoff. Downstream scalar-sector coefficients must then factor through the same parent response and matching prescription. A spectral-compression theorem gives a stronger sufficient condition: if a self-adjoint parent response contains exactly one unstable compact charged Lorentz-scalar two-plane with positive quartic stabilization, while all other charged scalar blocks are heavy or stable below the cutoff, the one-complex-scalar effective coordinate is generated by that single spectral block. The final section applies the criterion to the Axis Model as a conditional EFT closure audit. Using the cited Axis provenance ledger, the retained parent branch satisfies the one-field scalar audit within the stated parent-response class.
Scope
The criterion gives a one-field description when the specified parent response and common matching prescription satisfy its hypotheses. The Axis application is conditional on the response data cited in the paper. Physical sources, their normalization and boundary matching require independent construction; microscopic parent selection and predictions of gauge, gravitational or flavor observables remain open.
Paper and supporting files
The manuscript is available on Zenodo.
Read the current paper and supporting files on Zenodo