Flavor-Singlet Tetrad Condensation and Monometric Emergent Geometry: A Large-N Functional-RG Framework

Abstract

We investigate whether a multiflavor fermionic pregeometric framework can dynamically

select a single composite tetradic condensate from competing flavor channels. Within a

leading projected ladder/large-N functional-renormalization-group truncation, we analyze a

J = 2 channel whose dimensionless coupling obeys βg = 4g − ATg2, with AT > 0 under

the physical transverse-traceless susceptibility prescription adopted in the truncation. The

corresponding critical separatrix is g&lowast; = 4/AT. A flavor-dependent splitting permits the win

dow gS > g&lowast; >gA, so that the flavor singlet reaches the collective instability while a positive

subcritical adjoint branch remains below criticality. In the bosonized branch considered here,

singlet criticality is compatible with a nonzero tetradic condensate while the flavor-adjoint

directions retain positive quadratic curvature, yielding an operationally monometric phase

within the truncation. For a Hermitian physical transverse-traceless spin-2 channel with

nonzero spectral support and a well-defined subtracted dispersive representation, Källén

Lehmann positivity implies Zdisp

TT > 0. This result fixes only the dispersive contribution;

it does not determine local matching terms, the complete renormalized Planck coefficient,

or the full pole structure of the theory. The construction therefore provides a conditional

dynamical mechanism for selecting a single tetradic background from a multiflavor fermionic

system rather than a derivation of complete general relativity. Full Ward identities, local

matching, torsional dynamics, ghost tests outside the TT sector, and nonlinear completion

remain open problems for subsequent stages of the B-MECG research program

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BibTeX RIS

BibTeX

@misc{barrantes2026flavorsinglet,
  title = {{Flavor-Singlet Tetrad Condensation and Monometric Emergent Geometry: A Large-N Functional-RG Framework}},
  author = {Victor Barrantes},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23556292},
  url = {https://zenodo.org/records/23556292},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Flavor-Singlet Tetrad Condensation and Monometric Emergent Geometry: A Large-N Functional-RG Framework
AU  - Victor Barrantes
PY  - 2026
DA  - 2026/10/22
PB  - Zenodo
DO  - 10.5281/zenodo.23556292
UR  - https://zenodo.org/records/23556292
AB  - We investigate whether a multiflavor fermionic pregeometric framework can dynamically  select a single composite tetradic condensate from competing flavor channels. Within a  leading projected ladder/large-N functional-renormalization-group truncation, we analyze a  J = 2 channel whose dimensionless coupling obeys βg = 4g − ATg2, with AT > 0 under  the physical transverse-traceless susceptibility prescription adopted in the truncation. The  corresponding critical separatrix is g&lowast; = 4/AT. A flavor-dependent splitting permits the win  dow gS > g&lowast; >gA, so that the flavor singlet reaches the collective instability while a positive  subcritical adjoint branch remains below criticality. In the bosonized branch considered here,  singlet criticality is compatible with a nonzero tetradic condensate while the flavor-adjoint  directions retain positive quadratic curvature, yielding an operationally monometric phase  within the truncation. For a Hermitian physical transverse-traceless spin-2 channel with  nonzero spectral support and a well-defined subtracted dispersive representation, Källén  Lehmann positivity implies Zdisp  TT > 0. This result fixes only the dispersive contribution;  it does not determine local matching terms, the complete renormalized Planck coefficient,  or the full pole structure of the theory. The construction therefore provides a conditional  dynamical mechanism for selecting a single tetradic background from a multiflavor fermionic  system rather than a derivation of complete general relativity. Full Ward identities, local  matching, torsional dynamics, ghost tests outside the TT sector, and nonlinear completion  remain open problems for subsequent stages of the B-MECG research program
ER  -

Abstract

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