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April 8, 20260 citationsOpen Access

RG Stability of the Collective Membrane Fixed Point in the U-Cell Model: Exact Couplings and Infrared Attractor

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NPNorbert Prebeck

Key Points

  • The research aims to establish the infrared stability of the collective membrane fixed point in the U-cell model and derive relevant couplings.
  • Proved infrared stability of the collective membrane fixed point with θ = -1
  • Derived exact couplings g₀², κ̃₀, and αC from UCM substrate parameters
  • Reformulated Conjecture 2 into a non-perturbative conformal invariance condition
  • Established that three exact couplings are g₀² = 6/π, κ̃₀ = 1/(2π), and αC = 3/2
  • Ruled out perturbative methods to derive X = 61.5
  • Provided new perspectives on conformal invariance conditions.

Abstract

UCM Paper 33. Proves IR stability (θ = −1) of the collective membrane fixed point identified in Paper 32. Derives three exact couplings g₀² = 6/π, κ̃₀ = 1/(2π), αC = 3/2 from UCM substrate parameters. Rules out all perturbative derivations of X = 61.5 and reformulates Conjecture 2 as a non-perturbative conformal invariance condition.

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Cite This Study

Norbert Prebeck (2026) studied this question.

synapsesocial.com/papers/69d5f13674eaea4b11a7ac41https://doi.org/10.5281/zenodo.19439909
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