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

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